最 低 价：￥129.80
定 价：￥144.19
作 者：EdwardJamesMcShane 著 著
出 版 社：Oversea Publishing House
出版时间：2005-4-1
I S B N：9780486442358
| CHAPTER O-PRELIMINARIES 1.Sets 2.Functions and Relations 3.Natural Numbers and Integers 4.Disclaimer CHAPTER IREAL NUMBERS 1.Fields 2.Associativity, Commutativity, Distributivity 3.Ordered Fields 4.Isomorphism of Ordered Fields 5.Complete Ordered Fields 6.Uniqueness of Complete Ordered Fields 7.The Real Number System 8.Partially Ordered Sets 9.The Maximality Principle CHAPTER II-CONVERGENCE 1.Convergence of Real-Valued Functions 2.Elementary Properties 3.Subdirected Functions 4.Topological Spaces 5.Convergence in Topological Spaces 6.Product Spaces 7.Neighborhoods and Open Sets 8.Closed Sets 9.Relative Topologies 10.Compact Sets 11.Order-Convergence 12.Metric Spaces 13.Convergence in R CHAPTER III-CONTINUITY 1.Definition of Continuity 2.Functions on Topological Spaces 3.Semicontinuity 4.Uniform Continuity 5.Double Limits 6.Uniform Convergence 7.The Stone-Weierstrass Approximation Theorem 8.Ascoli's Theorem 9.Extensions of Functions CHAPTER IV-BOUNDED VARIATION, ABSOLUTE CONTINUITY, DIFFERENTIATION 1.Monotone Functions 2.Functions of Bounded Variation 3.Absolutely Continuous Functions 4.Functions of Intervals 5.Derivatives 6.Continuous Nowhere-Differentiable Functions 7.Taylor's Formula 8.Differentials 9.The Implicit Functions Theorem CHAPTER V-LEBESGUE-STIELTJES INTEGRATION 1.U-Functions and L-Functions 2.Properties of U-Functions and of L-Functions 3.The Integral 4.Convergence Theorems and Sets of Measure Zero 5.Summabilit and Intervals of Continuity 6.Fubini's Theorem 7.Measurable Functions 8.Measurable Sets 9.Integrals from Measures 10.Inequalities 11.The Riemann and Riemann-Stieltjes Integrals CHAPTER VI-THE INTEGRAL AS A FUNCTION OF SETS CHAPTER VII-THE Lp SPACES APPENDIX I-THE PRINCIPLE OF INDUCTIVE DEFINTION APPENDIX II-THE MAXIMALITY PRINCIPLE APPENDIX III-TYCHONOFF'S THEOREM BIBLIOGRAPHY SYMBOLS INDEX |
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