Lebesgue integration and measure

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Lebesgue integration and measure / Alan J. Weir

資料種別:: 図書
出版情報:: Cambridge : University Press, 1973
形態:: xii, 281 p. ; 24 cm
シリーズ名:: Integration and measure ; v. 1 <BA44798609>
著者名:: Weir, Alan J. <DA03214011>
ISBN:: 9780521087285 [0521087287]
9780521097512 [0521097517] (: pbk.)
書誌ID:: BA06846183

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注記:

Continued by General integration and measure
Bibliography: p. 277-278

主題:

Integrals, Generalized; Measure theory

言語:

英語

目次情報:

Preface

The Completeness of the Reals / 1：

The Axiom of Completeness / 1.1：

Infima and suprema / 1.2：

Postscript on the axioms for R / 1.3：

Null Sets / 2：

Countable sets / 2.1：

Null sets / 2.2：

Cantor's ternary set / 2.3：

The Lebesgue Integral on R / 3：

Step functions / 3.1：

Construction of the Lebesgue integral / 3.2：

Relation to the 'definite integral' / 3.3：

Relation to the 'indefinite integral' / 3.4：

Some further results / 3.5：

Step functions on R / 4：

The Lebesgue integral on R / 4.2：

Fubini's Theorem / 4.3：

The Convergence Theorems / 5：

The Monotone Convergence Theorem / 5.1：

The Dominated Convergence Theorem / 5.2：

Measurable Functions and Lebesgue Measure / 6：

Measurable functions / 6.1：

Lebesgue measure on R / 6.2：

The geometry of Lebesgue measure / 6.3：

Transformation of integrals / 6.4：

The Spaces L[superscript p] / 7：

The completeness of R as a metric space / 7.1：

The spaces L[superscript p] / 7.2：

The geometry of L[superscript 2] / 7.3：

Bounded linear functionals on L[suprescript 2] / 7.4：

Orthonormal sets in L[superscript 2] / 7.5：

Classical Fourier series / 7.6：

Reflections on Hilbert space / 7.7：

The elements of topology / Appendix：

Solutions

References

Index

The completeness of the reals

The Lebesgue integral on Rk

The convergence theorems

Measurable functions and Lebesgue measure

The spaces Lp

Appendix: the elements of topology

Preface

The Completeness of the Reals / 1：

The Axiom of Completeness / 1.1：

Infima and suprema / 1.2：

Postscript on the axioms for R / 1.3：

Null Sets / 2：

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