A course on Borel sets.

*(English)*Zbl 0903.28001
Graduate Texts in Mathematics. 180. New York, NY: Springer. xvi, 261 p. (1998).

This is a very clearly written book concerning an introduction to the classical theory of Borel sets and measurable selections. The book is divided onto five chapters that contain: Chapter 1 – set theoretic preliminaries (ordinal and cardinal numbers, alephs, trees and the Souslin operation); Chapter 2 – topological preliminaries (Polish spaces, the Baire space \(N^N\), the Cantor space \(2^N\), and some theorems that help in transforming many problems from general Polish spaces to the Baire space or to the Cantor space); Chapter 3 – the hierarchy and properties of Borel sets (universal sets, reduction and separation theorems); Chapter 4 – basic properties of analytic and coanalytic sets; Chapter 5 – most of the major measurable selection and uniformization theorems that are important for applications. The book contains also a large number of interesting excercises.

Reviewer: T. Natkaniec (Gdańsk)

##### MSC:

28-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration |

28A05 | Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets |

03-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations |

03E15 | Descriptive set theory |

54H05 | Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) |