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...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2001
|
| Series: | Cambridge tracts in mathematics
140 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (xvi, 266 Seiten) |
| ISBN: | 9780511574764 |
| DOI: | 10.1017/CBO9780511574764 |
Staff View
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| 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 | ||
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Record in the Search Index
| _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 |
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| 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 |
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| 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 |