Springer Book Archives: eBooks only 8.99 each! Save now >>

Graduate Texts in Mathematics

A Course on Borel Sets

Authors: Srivastava, S.M.

Free Preview

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-642-85473-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
About this Textbook

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 Dirich­ let 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 con­ tinuous functions and iterating the operation 0/ pointwise limit on a se­ quence 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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-642-85473-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
A Course on Borel Sets
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
180
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-85473-6
DOI
10.1007/978-3-642-85473-6
Series ISSN
0072-5285
Edition Number
1
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works are not included.