This book offers several topics of mathematical analysis which are closely connected with significant properties of real-valued functions of various types (such as semi-continuous functions, monotone functions, convex functions, measurable functions, additive and linear functionals, etc.). Alongside with fairly traditional themes of real analysis and classical measure theory, more profound questions are thoroughly discussed in the book - appropriate extensions and restrictions of functions, oscillation functions and their characterization, discontinuous functions on resolvable topological spaces, pointwise limits of finite sums of periodic functions, some general results on invariant and quasi-invariant measures, the structure of non-measurable sets and functions, the Baire property of functions on topological spaces and its connections with measurability properties of functions, logical and set-theoretical aspects of the behavior of real-valued functions.

Autorentext

Alexander Kharazishvili is a chief researcher at the A. Razmadze Mathematical Institute of Tbilisi State University and a member of the Georgian National Academy of Sciences. His research interests mainly concern real analysis and measure theory, mostly with various properties of real-valued functions such as topological, algebraic, measure-theoretical, etc. He has more than 300 scientific publications and is the author of the book "Strange Functions in Real Analysis", published by CRC Press. The third edition of this book was published in 2018.