Measure and Integration: An Introductory Path Toward Functional Analysis and Probability (Cornerstones)

This textbook provides a thorough exposition of measure and integration theory in a style that is very detailed and thus easy to follow and understand.While breaking down argumentation to simple steps and maintaining a consistent exposition, the book presents the theory on a high level of scientific rigor and generality. Although the book covers a wide spectrum of topics, it leads to a path in functional analysis and probability theory.Thus, a full chapter on measures with densities, including Lebesgue decomposition and Radon-Nikodym's theorem, is included, as well as a chapter on transformation of measures, which is a crucial topic in probability theory.Chapters on Hilbert spaces and the Fourier transform prepare the way for a direction in functional analysis.The book features also a presentation of the Cauchy-Stieltjes transform, which is an alternative to the Fourier transform and highly used in some branches of mathematics, like mathematical physics and random matrix theory. The te