Topics in the Theory of Lifting:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1969
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
48 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The problem as to whether or not there exists a lifting of the M't/. 1 space ) corresponding to the real line and Lebesgue measure on it was first raised by A. Haar. It was solved in a paper published in 1931 [102] by 1. von Neumann, who established the existence of a lifting in this case. In subsequent papers J. von Neumann and M. H. Stone [105], and later on 1. Dieudonne [22], discussed various algebraic aspects and generalizations of the problem. Attemps to solve the problem as to whether or not there exists a lifting for an arbitrary M't/. space were unsuccessful for a long time, although the problem had significant connections with other branches of mathematics. Finally, in a paper published in 1958 [88], D. Maharam established, by a delicate argument, that a lifting of M't/. always exists (for an arbi trary space of a-finite mass). D. Maharam proved first the existence of a lifting of the M't/. space corresponding to a product X = TI {ai,b,} ieI and a product measure J.1= Q9 J.1i' with J.1i{a;}=J.1i{b,}=! for all iE/. ,eI Then, she reduced the general case to this one, via an isomorphism theorem concerning homogeneous measure algebras [87], [88]. A different and more direct proof of the existence of a lifting was subsequently given by the authors in [65]' A variant of this proof is presented in chapter 4 |
| Physical Description: | 1 Online-Ressource (X, 192 p) |
| ISBN: | 9783642885075 9783642885099 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-88507-5 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423099 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1969 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642885075 |c Online |9 978-3-642-88507-5 | ||
| 020 | |a 9783642885099 |c Print |9 978-3-642-88509-9 | ||
| 024 | 7 | |a 10.1007/978-3-642-88507-5 |2 doi | |
| 035 | |a (OCoLC)905372063 | ||
| 035 | |a (DE-599)BVBBV042423099 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Tulcea, A. Ionescu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topics in the Theory of Lifting |c by A. Ionescu Tulcea, C. Ionescu Tulcea |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1969 | |
| 300 | |a 1 Online-Ressource (X, 192 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 48 |x 0071-1136 | |
| 500 | |a The problem as to whether or not there exists a lifting of the M't/. 1 space ) corresponding to the real line and Lebesgue measure on it was first raised by A. Haar. It was solved in a paper published in 1931 [102] by 1. von Neumann, who established the existence of a lifting in this case. In subsequent papers J. von Neumann and M. H. Stone [105], and later on 1. Dieudonne [22], discussed various algebraic aspects and generalizations of the problem. Attemps to solve the problem as to whether or not there exists a lifting for an arbitrary M't/. space were unsuccessful for a long time, although the problem had significant connections with other branches of mathematics. Finally, in a paper published in 1958 [88], D. Maharam established, by a delicate argument, that a lifting of M't/. always exists (for an arbi trary space of a-finite mass). D. Maharam proved first the existence of a lifting of the M't/. space corresponding to a product X = TI {ai,b,} ieI and a product measure J.1= Q9 J.1i' with J.1i{a;}=J.1i{b,}=! for all iE/. ,eI Then, she reduced the general case to this one, via an isomorphism theorem concerning homogeneous measure algebras [87], [88]. A different and more direct proof of the existence of a lifting was subsequently given by the authors in [65]' A variant of this proof is presented in chapter 4 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Theorie |0 (DE-588)4059787-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Liften |g Mathematik |0 (DE-588)4167655-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Liften |g Mathematik |0 (DE-588)4167655-5 |D s |
| 689 | 0 | 1 | |a Theorie |0 (DE-588)4059787-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Tulcea, C. Ionescu |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-88507-5 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858516 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153098445258752 |
|---|---|
| any_adam_object | |
| author | Tulcea, A. Ionescu |
| author_facet | Tulcea, A. Ionescu |
| author_role | aut |
| author_sort | Tulcea, A. Ionescu |
| author_variant | a i t ai ait |
| building | Verbundindex |
| bvnumber | BV042423099 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)905372063 (DE-599)BVBBV042423099 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-88507-5 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03026nmm a2200481zcb4500</leader><controlfield tag="001">BV042423099</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1969 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642885075</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-88507-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642885099</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-88509-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-88507-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)905372063</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423099</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Tulcea, A. Ionescu</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Topics in the Theory of Lifting</subfield><subfield code="c">by A. Ionescu Tulcea, C. Ionescu Tulcea</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1969</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (X, 192 p)</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">Ergebnisse der Mathematik und ihrer Grenzgebiete</subfield><subfield code="v">48</subfield><subfield code="x">0071-1136</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The problem as to whether or not there exists a lifting of the M't/. 1 space ) corresponding to the real line and Lebesgue measure on it was first raised by A. Haar. It was solved in a paper published in 1931 [102] by 1. von Neumann, who established the existence of a lifting in this case. In subsequent papers J. von Neumann and M. H. Stone [105], and later on 1. Dieudonne [22], discussed various algebraic aspects and generalizations of the problem. Attemps to solve the problem as to whether or not there exists a lifting for an arbitrary M't/. space were unsuccessful for a long time, although the problem had significant connections with other branches of mathematics. Finally, in a paper published in 1958 [88], D. Maharam established, by a delicate argument, that a lifting of M't/. always exists (for an arbi trary space of a-finite mass). D. Maharam proved first the existence of a lifting of the M't/. space corresponding to a product X = TI {ai,b,} ieI and a product measure J.1= Q9 J.1i' with J.1i{a;}=J.1i{b,}=! for all iE/. ,eI Then, she reduced the general case to this one, via an isomorphism theorem concerning homogeneous measure algebras [87], [88]. A different and more direct proof of the existence of a lifting was subsequently given by the authors in [65]' A variant of this proof is presented in chapter 4</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Theorie</subfield><subfield code="0">(DE-588)4059787-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Liften</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4167655-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Liften</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4167655-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Theorie</subfield><subfield code="0">(DE-588)4059787-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tulcea, C. Ionescu</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-88507-5</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858516</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042423099 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642885075 9783642885099 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858516 |
| oclc_num | 905372063 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 192 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Tulcea, A. Ionescu Verfasser aut Topics in the Theory of Lifting by A. Ionescu Tulcea, C. Ionescu Tulcea Berlin, Heidelberg Springer Berlin Heidelberg 1969 1 Online-Ressource (X, 192 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 48 0071-1136 The problem as to whether or not there exists a lifting of the M't/. 1 space ) corresponding to the real line and Lebesgue measure on it was first raised by A. Haar. It was solved in a paper published in 1931 [102] by 1. von Neumann, who established the existence of a lifting in this case. In subsequent papers J. von Neumann and M. H. Stone [105], and later on 1. Dieudonne [22], discussed various algebraic aspects and generalizations of the problem. Attemps to solve the problem as to whether or not there exists a lifting for an arbitrary M't/. space were unsuccessful for a long time, although the problem had significant connections with other branches of mathematics. Finally, in a paper published in 1958 [88], D. Maharam established, by a delicate argument, that a lifting of M't/. always exists (for an arbi trary space of a-finite mass). D. Maharam proved first the existence of a lifting of the M't/. space corresponding to a product X = TI {ai,b,} ieI and a product measure J.1= Q9 J.1i' with J.1i{a;}=J.1i{b,}=! for all iE/. ,eI Then, she reduced the general case to this one, via an isomorphism theorem concerning homogeneous measure algebras [87], [88]. A different and more direct proof of the existence of a lifting was subsequently given by the authors in [65]' A variant of this proof is presented in chapter 4 Mathematics Mathematics, general Mathematik Theorie (DE-588)4059787-8 gnd rswk-swf Liften Mathematik (DE-588)4167655-5 gnd rswk-swf Liften Mathematik (DE-588)4167655-5 s Theorie (DE-588)4059787-8 s 1\p DE-604 Tulcea, C. Ionescu Sonstige oth https://doi.org/10.1007/978-3-642-88507-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tulcea, A. Ionescu Topics in the Theory of Lifting Mathematics Mathematics, general Mathematik Theorie (DE-588)4059787-8 gnd Liften Mathematik (DE-588)4167655-5 gnd |
| subject_GND | (DE-588)4059787-8 (DE-588)4167655-5 |
| title | Topics in the Theory of Lifting |
| title_auth | Topics in the Theory of Lifting |
| title_exact_search | Topics in the Theory of Lifting |
| title_full | Topics in the Theory of Lifting by A. Ionescu Tulcea, C. Ionescu Tulcea |
| title_fullStr | Topics in the Theory of Lifting by A. Ionescu Tulcea, C. Ionescu Tulcea |
| title_full_unstemmed | Topics in the Theory of Lifting by A. Ionescu Tulcea, C. Ionescu Tulcea |
| title_short | Topics in the Theory of Lifting |
| title_sort | topics in the theory of lifting |
| topic | Mathematics Mathematics, general Mathematik Theorie (DE-588)4059787-8 gnd Liften Mathematik (DE-588)4167655-5 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Theorie Liften Mathematik |
| url | https://doi.org/10.1007/978-3-642-88507-5 |
| work_keys_str_mv | AT tulceaaionescu topicsinthetheoryoflifting AT tulceacionescu topicsinthetheoryoflifting |