This book is concerned with a certain circle of questions from classical real analysis and measure theory. First, we would like to stress that the choice of topics presented in the text is completely dictated by our research interests and preferences. Nevertheless, we hope that this material will be of interest to a (more or less) wide audience of mathematicians, especially to those working in various branches of modern mathematical analysis, probability theory, the theory of stochastic processes, and general topology.We also touch upon set-theoretical aspects of themes discussed in the book. Perhaps, some of these ideas will be interesting for set-theorists and will help them to find new applications of their methods to various problems of real analysis and measure theory.
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