Set Theoretical Aspects Of Real Analysis
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Set Theoretical Aspects of Real Analysis
Author: Alexander B. Kharazishvili
language: en
Publisher: CRC Press
Release Date: 2014-08-26
Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary b
Applications of Point Set Theory in Real Analysis
Author: A.B. Kharazishvili
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line. Notice that various topics from this theory are presented in several books and surveys. From among the most important works devoted to Point Set Theory, let us first of all mention the excellent book by Oxtoby [83] in which a deep analogy between measure and category is discussed in detail. Further, an interesting general approach to problems concerning measure and category is developed in the well-known monograph by Morgan [79] where a fundamental concept of a category base is introduced and investigated. We also wish to mention that the monograph by Cichon, W«;glorz and the author [19] has recently been published. In that book, certain classes of subsets of the real line are studied and various cardinal valued functions (characteristics) closely connected with those classes are investigated. Obviously, the IT-ideal of all Lebesgue measure zero subsets of the real line and the IT-ideal of all first category subsets of the same line are extensively studied in [19], and several relatively new results concerning this topic are presented. Finally, it is reasonable to notice here that some special sets of points, the so-called singular spaces, are considered in the classi
Real Analysis Through Modern Infinitesimals
Author: Nader Vakil
language: en
Publisher: Cambridge University Press
Release Date: 2011-02-17
A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.