A Course on Borel Sets:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1998
|
| Series: | Graduate Texts in Mathematics
180 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirichlet and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from continuous functions and iterating the operation 0/ pointwise limit on a sequence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783642854736 9783642854750 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-3-642-85473-6 |
Staff View
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| 500 | |a The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirichlet and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from continuous functions and iterating the operation 0/ pointwise limit on a sequence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire | ||
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| isbn | 9783642854736 9783642854750 |
| issn | 0072-5285 |
| language | English |
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| spelling | Srivastava, S. M. Verfasser aut A Course on Borel Sets by S. M. Srivastava Berlin, Heidelberg Springer Berlin Heidelberg 1998 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 180 0072-5285 The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirichlet and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from continuous functions and iterating the operation 0/ pointwise limit on a sequence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire Mathematics Logic, Symbolic and mathematical Topology Mathematical Logic and Foundations Mathematik Borel-Menge (DE-588)4146323-7 gnd rswk-swf Borel-Menge (DE-588)4146323-7 s 1\p DE-604 Graduate Texts in Mathematics 180 (DE-604)BV035421258 180 https://doi.org/10.1007/978-3-642-85473-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Srivastava, S. M. A Course on Borel Sets Graduate Texts in Mathematics Mathematics Logic, Symbolic and mathematical Topology Mathematical Logic and Foundations Mathematik Borel-Menge (DE-588)4146323-7 gnd |
| subject_GND | (DE-588)4146323-7 |
| title | A Course on Borel Sets |
| title_auth | A Course on Borel Sets |
| title_exact_search | A Course on Borel Sets |
| title_full | A Course on Borel Sets by S. M. Srivastava |
| title_fullStr | A Course on Borel Sets by S. M. Srivastava |
| title_full_unstemmed | A Course on Borel Sets by S. M. Srivastava |
| title_short | A Course on Borel Sets |
| title_sort | a course on borel sets |
| topic | Mathematics Logic, Symbolic and mathematical Topology Mathematical Logic and Foundations Mathematik Borel-Menge (DE-588)4146323-7 gnd |
| topic_facet | Mathematics Logic, Symbolic and mathematical Topology Mathematical Logic and Foundations Mathematik Borel-Menge |
| url | https://doi.org/10.1007/978-3-642-85473-6 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT srivastavasm acourseonborelsets |