Mezijar Views Read Edit View history. Following is Theorem 4. Hewitt pioneered the construction of the hyperreals by means stromverg an ultrapower construction Hewitt, Post as a guest Name. He received his Ph. Search this index Full-text Catalog. One classical example is an infinite analysiss which cannot be written as a disjoint union of two infinite sets meaning, every subset is finite or its complement is finite.
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The level of abstraction referred to in the second half of the title is not very high: the book deals with general measure spaces but is otherwise not very abstract.
It has a moderate amount of material on function spaces, but these are presented to aid the work on integration and differentiation and not as subjects in themselves. For example, the book uses the Daniell approach to integration through functionals rather than defining integrals directly in terms of measures.
Scattered throughout the book is a lot of material on Fourier analysis, although only on the real line. The book has an excellent index and is more of a reference than a text. The sequence of theorems is very well organized, so that no individual proof is very long but also every theorem is useful or interesting. Another good book that also covers generally the same topics but is more abstract and perhaps more modern is Gert K.
Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds. His mathematical interests are number theory and classical analysis. The algebra of sets Section 2. Relations and functions Section 3. The axiom of choice and some equivalents Section 4. Cardinal numbers and ordinal numbers Section 5. Topological preliminaries Section 7. The Riemann-Stieltjes integral Section 9.
Extending certain functionals Section Measures and measurable sets Section Measurable functions Section Abstract Banach spaces Section Differentiable and nondifferentiable functions Section Absolutely continuous functions Section Complex measures and the Lebesgue-Radon-Nikodym theorem Section The product of two measure spaces Section
Real and abstract analysis
Real and Abstract Analysis