Derivation and integration:
This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2001
|
| Schriftenreihe: | Cambridge tracts in mathematics
140 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A very general Gauss-Green theorem follows from the sufficient conditions for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas |
| Beschreibung: | 1 Online-Ressource (xvi, 266 Seiten) |
| ISBN: | 9780511574764 |
| DOI: | 10.1017/CBO9780511574764 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941815 | ||
| 003 | DE-604 | ||
| 005 | 20190429 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2001 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511574764 |c Online |9 978-0-511-57476-4 | ||
| 024 | 7 | |a 10.1017/CBO9780511574764 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511574764 | ||
| 035 | |a (OCoLC)967683819 | ||
| 035 | |a (DE-599)BVBBV043941815 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-355 | ||
| 082 | 0 | |a 515/.4 |2 21 | |
| 084 | |a SK 400 |0 (DE-625)143237: |2 rvk | ||
| 084 | |a SK 430 |0 (DE-625)143239: |2 rvk | ||
| 100 | 1 | |a Pfeffer, Washek F. |d 1936- |e Verfasser |0 (DE-588)1025828372 |4 aut | |
| 245 | 1 | 0 | |a Derivation and integration |c Washek F. Pfeffer |
| 246 | 1 | 3 | |a Derivation & Integration |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2001 | |
| 300 | |a 1 Online-Ressource (xvi, 266 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge tracts in mathematics |v 140 | |
| 505 | 8 | 0 | |t Topology |t Measures |t Covering theorems |t Densities |t Lipschitz maps |t BV functions |t BV sets |t Slices of BV sets |t Approximating BV sets |t Charges |t The definition and examples |t Spaces of charges |t Derivates |t Derivability |t Reduced charges |t Partitions |t Variations of charges |t Some classical concepts |t The essential variation |t The integration problem |t An excursion to Hausdorff measures |t The critical variation |t AC[subscript *] charges |t Essentially clopen sets |t Charges and BV functions |t The charge F x L[superscript 1] |t The space (CH[subscript *](E), S) |t Duality |t More on BV functions |t The charge F [angle] g |t Lipeomorphisms |t Integration |t The R-integral |t Multipliers |t Change of variables |t Averaging |t The Riemann approach |t Charges as distributional derivatives |t The Lebesgue integral |t Extending the integral |t Buczolich's example |t I-convergence |t The GR-integral |t Additional properties |
| 520 | |a This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A very general Gauss-Green theorem follows from the sufficient conditions for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas | ||
| 650 | 4 | |a Integrals, Generalized | |
| 650 | 0 | 7 | |a Verallgemeinerung |0 (DE-588)4316262-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integral |0 (DE-588)4131477-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Integral |0 (DE-588)4131477-3 |D s |
| 689 | 0 | 1 | |a Verallgemeinerung |0 (DE-588)4316262-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-521-15565-6 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-521-79268-4 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511574764 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029350785 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9780511574764 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511574764 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511574764 |l UBR01 |p ZDB-20-CBO |q UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176884005601280 |
|---|---|
| any_adam_object | |
| author | Pfeffer, Washek F. 1936- |
| author_GND | (DE-588)1025828372 |
| author_facet | Pfeffer, Washek F. 1936- |
| author_role | aut |
| author_sort | Pfeffer, Washek F. 1936- |
| author_variant | w f p wf wfp |
| building | Verbundindex |
| bvnumber | BV043941815 |
| classification_rvk | SK 400 SK 430 |
| collection | ZDB-20-CBO |
| contents | Topology Measures Covering theorems Densities Lipschitz maps BV functions BV sets Slices of BV sets Approximating BV sets Charges The definition and examples Spaces of charges Derivates Derivability Reduced charges Partitions Variations of charges Some classical concepts The essential variation The integration problem An excursion to Hausdorff measures The critical variation AC[subscript *] charges Essentially clopen sets Charges and BV functions The charge F x L[superscript 1] The space (CH[subscript *](E), S) Duality More on BV functions The charge F [angle] g Lipeomorphisms Integration The R-integral Multipliers Change of variables Averaging The Riemann approach Charges as distributional derivatives The Lebesgue integral Extending the integral Buczolich's example I-convergence The GR-integral Additional properties |
| ctrlnum | (ZDB-20-CBO)CR9780511574764 (OCoLC)967683819 (DE-599)BVBBV043941815 |
| dewey-full | 515/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.4 |
| dewey-search | 515/.4 |
| dewey-sort | 3515 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511574764 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03906nmm a2200517zcb4500</leader><controlfield tag="001">BV043941815</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190429 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2001 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511574764</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-57476-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511574764</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511574764</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)967683819</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941815</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.4</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 400</subfield><subfield code="0">(DE-625)143237:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 430</subfield><subfield code="0">(DE-625)143239:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pfeffer, Washek F.</subfield><subfield code="d">1936-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1025828372</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Derivation and integration</subfield><subfield code="c">Washek F. Pfeffer</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Derivation & Integration</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xvi, 266 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge tracts in mathematics</subfield><subfield code="v">140</subfield></datafield><datafield tag="505" ind1="8" ind2="0"><subfield code="t">Topology</subfield><subfield code="t">Measures</subfield><subfield code="t">Covering theorems</subfield><subfield code="t">Densities</subfield><subfield code="t">Lipschitz maps</subfield><subfield code="t">BV functions</subfield><subfield code="t">BV sets</subfield><subfield code="t">Slices of BV sets</subfield><subfield code="t">Approximating BV sets</subfield><subfield code="t">Charges</subfield><subfield code="t">The definition and examples</subfield><subfield code="t">Spaces of charges</subfield><subfield code="t">Derivates</subfield><subfield code="t">Derivability</subfield><subfield code="t">Reduced charges</subfield><subfield code="t">Partitions</subfield><subfield code="t">Variations of charges</subfield><subfield code="t">Some classical concepts</subfield><subfield code="t">The essential variation</subfield><subfield code="t">The integration problem</subfield><subfield code="t">An excursion to Hausdorff measures</subfield><subfield code="t">The critical variation</subfield><subfield code="t">AC[subscript *] charges</subfield><subfield code="t">Essentially clopen sets</subfield><subfield code="t">Charges and BV functions</subfield><subfield code="t">The charge F x L[superscript 1]</subfield><subfield code="t">The space (CH[subscript *](E), S)</subfield><subfield code="t">Duality</subfield><subfield code="t">More on BV functions</subfield><subfield code="t">The charge F [angle] g</subfield><subfield code="t">Lipeomorphisms</subfield><subfield code="t">Integration</subfield><subfield code="t">The R-integral</subfield><subfield code="t">Multipliers</subfield><subfield code="t">Change of variables</subfield><subfield code="t">Averaging</subfield><subfield code="t">The Riemann approach</subfield><subfield code="t">Charges as distributional derivatives</subfield><subfield code="t">The Lebesgue integral</subfield><subfield code="t">Extending the integral</subfield><subfield code="t">Buczolich's example</subfield><subfield code="t">I-convergence</subfield><subfield code="t">The GR-integral</subfield><subfield code="t">Additional properties</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A very general Gauss-Green theorem follows from the sufficient conditions for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integrals, Generalized</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Verallgemeinerung</subfield><subfield code="0">(DE-588)4316262-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Verallgemeinerung</subfield><subfield code="0">(DE-588)4316262-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-521-15565-6</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-521-79268-4</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511574764</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350785</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511574764</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511574764</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511574764</subfield><subfield code="l">UBR01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UBR Einzelkauf (Lückenergänzung CUP Serien 2018)</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043941815 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511574764 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350785 |
| oclc_num | 967683819 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xvi, 266 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Pfeffer, Washek F. 1936- Verfasser (DE-588)1025828372 aut Derivation and integration Washek F. Pfeffer Derivation & Integration Cambridge Cambridge University Press 2001 1 Online-Ressource (xvi, 266 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 140 Topology Measures Covering theorems Densities Lipschitz maps BV functions BV sets Slices of BV sets Approximating BV sets Charges The definition and examples Spaces of charges Derivates Derivability Reduced charges Partitions Variations of charges Some classical concepts The essential variation The integration problem An excursion to Hausdorff measures The critical variation AC[subscript *] charges Essentially clopen sets Charges and BV functions The charge F x L[superscript 1] The space (CH[subscript *](E), S) Duality More on BV functions The charge F [angle] g Lipeomorphisms Integration The R-integral Multipliers Change of variables Averaging The Riemann approach Charges as distributional derivatives The Lebesgue integral Extending the integral Buczolich's example I-convergence The GR-integral Additional properties This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A very general Gauss-Green theorem follows from the sufficient conditions for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas Integrals, Generalized Verallgemeinerung (DE-588)4316262-9 gnd rswk-swf Integral (DE-588)4131477-3 gnd rswk-swf Integral (DE-588)4131477-3 s Verallgemeinerung (DE-588)4316262-9 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-15565-6 Erscheint auch als Druck-Ausgabe 978-0-521-79268-4 https://doi.org/10.1017/CBO9780511574764 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Pfeffer, Washek F. 1936- Derivation and integration Topology Measures Covering theorems Densities Lipschitz maps BV functions BV sets Slices of BV sets Approximating BV sets Charges The definition and examples Spaces of charges Derivates Derivability Reduced charges Partitions Variations of charges Some classical concepts The essential variation The integration problem An excursion to Hausdorff measures The critical variation AC[subscript *] charges Essentially clopen sets Charges and BV functions The charge F x L[superscript 1] The space (CH[subscript *](E), S) Duality More on BV functions The charge F [angle] g Lipeomorphisms Integration The R-integral Multipliers Change of variables Averaging The Riemann approach Charges as distributional derivatives The Lebesgue integral Extending the integral Buczolich's example I-convergence The GR-integral Additional properties Integrals, Generalized Verallgemeinerung (DE-588)4316262-9 gnd Integral (DE-588)4131477-3 gnd |
| subject_GND | (DE-588)4316262-9 (DE-588)4131477-3 |
| title | Derivation and integration |
| title_alt | Derivation & Integration Topology Measures Covering theorems Densities Lipschitz maps BV functions BV sets Slices of BV sets Approximating BV sets Charges The definition and examples Spaces of charges Derivates Derivability Reduced charges Partitions Variations of charges Some classical concepts The essential variation The integration problem An excursion to Hausdorff measures The critical variation AC[subscript *] charges Essentially clopen sets Charges and BV functions The charge F x L[superscript 1] The space (CH[subscript *](E), S) Duality More on BV functions The charge F [angle] g Lipeomorphisms Integration The R-integral Multipliers Change of variables Averaging The Riemann approach Charges as distributional derivatives The Lebesgue integral Extending the integral Buczolich's example I-convergence The GR-integral Additional properties |
| title_auth | Derivation and integration |
| title_exact_search | Derivation and integration |
| title_full | Derivation and integration Washek F. Pfeffer |
| title_fullStr | Derivation and integration Washek F. Pfeffer |
| title_full_unstemmed | Derivation and integration Washek F. Pfeffer |
| title_short | Derivation and integration |
| title_sort | derivation and integration |
| topic | Integrals, Generalized Verallgemeinerung (DE-588)4316262-9 gnd Integral (DE-588)4131477-3 gnd |
| topic_facet | Integrals, Generalized Verallgemeinerung Integral |
| url | https://doi.org/10.1017/CBO9780511574764 |
| work_keys_str_mv | AT pfefferwashekf derivationandintegration AT pfefferwashekf derivationintegration |