It is well known that by the term "Practical Analysis" we no longer mean the area of mathematics that deals with the theory of functions of one or many variables but various (mostly abstract) branches of Mathematical Analysis. "Real Analysis" or "Abstract Analysis" or even "Modern Analysis", which is taught in all mathematics departments of the Universities either as a compulsory or as an elective course, is a course of rigorously based mathematical analysis that gives generalizations of many known concepts of which contributed to the leapfrog development of this field of mathematics. "Practice Analysis" does not encompass a fully defined content, with the result that a variety of concepts are observed in the relevant literature.
The purpose of the book is to help the students of the mathematics departments, on the one hand, to understand the basic and central concepts of the course in question (metric spaces, compactness, special sets, measurable functions, measures, Lebesgue integral, etc., etc.). l.) and on the other hand to gain an experience in solving the related exercises.
The book contains the basic definitions and key theorems that form the core of Real Analysis and (most importantly) five topic groups. The topics of each group cover a wide range of concepts related to the respective heading. A part of these topics has been prepared by the author of the book, several topics have been selected from the Greek and foreign literature, while topics that were given in undergraduate and qualifying exams of mathematics departments of Greek and foreign Universities are also included.