This 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 in between them. The material covered in this book will be of interest to a wide audience of mathematicians, in particular to those who are 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 reals and the ZFC axioms, Martin's axiom, and the continuum hypothesis. weiterlesen