A Course on Borel Sets [Hardcover]

A thorough introduction to Borel sets and measurable selections, acting as a stepping stone to descriptive set theory by presenting such important techniques as universal sets, prewellordering, scales, etc. It contains significant applications to other branches of mathematics and serves as a self-contained reference accessible by mathematicians in many different disciplines. Written in an easily understandable style, and using only naive set theory, general topology, analysis, and algebra, it is thus well suited for graduates exploring areas of mathematics for their research and for those requiring Borel sets and measurable selections in their work.A Course on Borel sets provides a thorough introduction to Borel sets and measurable selections and acts as a stepping stone to descriptive set theory by presenting important techniques such as universal sets, prewellordering, scales, etc. It is well suited for graduate students exploring areas of mathematics for their research and for mathematicians requiring Borel sets and measurable selections in their work. It contains significant applications to other branches of mathematics and can serve as a self- contained reference accessible by mathematicians in many different disciplines. It is written in an easily understandable style and employs only naive set theory, general topology, analysis, and algebra. A large number of interesting exercises are given throughout the text.Cardinal and Ordinal Numbers.- Topological Preliminaries.- Standard Borel Spaces.- Analytic and Coanalytic Sets.- Selection and Uniformization Theorems.* Takes the reader from the beginning of the subject all the way to harder theorems. * A thorough introduction to the concept of Borel sets which has important applications in other areas of analysis. * Treatment is geared for those interested in descriptive set theory and acts as a stepping stone to prepare one for working in the area.A Course on Borel sets provides a thorough introduction to Borel setslă