Set Theoretical Aspects of Real Analysis
Chapman & Hall/CRC (Verlag)
978-1-4822-4201-0 (ISBN)
The book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Lebesque measure theory that highlights the fundamental concepts of measurability and non-measurability for point sets and functions. Provided in the book are problems of varying difficulty that range from simple observations to advanced results. Relatively difficult exercises are marked by asterisks and hints are included with additional explanation. Five appendices are included to supply additional background information that can be read alongside, before, or after the chapters.
Dealing with classical concepts, the book highlights material not often found in analysis courses. It lays out, in a logical, systematic manner, the foundations of set theory providing a readable treatment accessible to graduate students and researchers.
Alexander B. Kharazishvili
ZF theory and some point sets on the real line. Countable versions of AC and real analysis. Uncountable versions of AC and Lebesgue nonmeasurable sets. The Continuum Hypothesis and Lebesgue nonmeasurable sets. Measurability properties of sets and functions. Radon measures and nonmeasurable sets. Real-valued step functions with strange measurability properties. Relationships between certain classical constructions of Lebesgue nonmeasurable sets. Measurability properties of Vitali sets. A relationship between the measurability and continuity of real-valued functions. A relationship between absolutely nonmeasurable functions and Sierpinski-Zygmund functions. Sums of absolutely nonmeasurable injective functions. A large group of absolutely nonmeasurable additive functions. Additive properties of certain classes of pathological functions. Absolutely nonmeasurable homomorphisms of commutative groups. Measurable and nonmeasurable sets with homogeneous sections. A combinatorial problem on translation invariant extensions of the Lebesgue measure. Countable almost invariant partitions of G-spaces. Nonmeasurable unions of measure zero sections of plane sets. Measurability properties of well-orderings. Appendices. Bibliography. Subject Index.
Reihe/Serie | Chapman & Hall/CRC Monographs and Research Notes in Mathematics |
---|---|
Sprache | englisch |
Maße | 156 x 234 mm |
Gewicht | 771 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
ISBN-10 | 1-4822-4201-X / 148224201X |
ISBN-13 | 978-1-4822-4201-0 / 9781482242010 |
Zustand | Neuware |
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