Author | Hewitt, Edwin. author |
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Title | Real and Abstract Analysis [electronic resource] : A modern treatment of the theory of functions of a real variable / by Edwin Hewitt, Karl Stromberg |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1965 |
Connect to | http://dx.doi.org/10.1007/978-3-642-88044-5 |
Descript | VIII, 476 p. online resource |
One: Set Theory and Algebra -- Section 1. 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. Construction of the real and complex number fields -- Two: Topology and Continuous Functions -- Section 6. Topological preliminaries -- Section 7. Spaces of continuous functions -- Three: The Lebesgue Integral -- Section 8. The Riemann-Stieltjes integral -- Section 9. Extending certain functionals -- Section 10. Measures and measurable sets -- Section 11. Measurable functions -- Section 12. The abstract Lebesgue integral -- Four: Function Spaces and Banach Spaces -- Section 13. The spaces $${\mathcal{L}_p}(1 \leqq p < \infty )$$ -- Section 14. Abstract Banach spaces -- Section 15. The conjugate space of $${\mathcal{L}_p}(1 < p < \infty )$$ -- Section 16. Abstract Hilbert spaces -- Five: Differentiation -- Section 17. Differentiable and nondifferentiable functions -- Section 18. Absolutely continuous functions -- Section 19. Complex measures and the Lebesgue-Radon-Nikodรฝm theorem -- Section 20. Applications of the Lebesgue-Radon-Nikodรฝm theorem -- Six: Integration on Product Spaces -- Section 21. The product of two measure spaces -- Section 22. Products of infinitely many measure spaces -- Index of Symbols -- Index of Authors and Terms