“This monograph deals with classical topics of real analysis and measure theory which show a number of interesting phenomena. … This makes the presented material useful and inspiring. … Every chapter is finished with a solid portion of exercises … of various difficulty. More advanced exercises are enriched with hints and comments.” (Marek Balcerzak, Mathematical Reviews, June, 2023)
“The text is mostly self-contained and at the end of each chapter are exercises providing additional information to the presented topic. It makes the book accessible to graduate and post-graduate students.” (Jaroslav Tišer, zbMATH 1504.26003, 2023)
Notes on Real Analysis and Measure Theory
Fine Properties of Real Sets and Functions
von Alexander KharazishviliThis monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
