Measure and integral  v. 1

John L. Kelley, T.P. Srinivasan

This book is a systematic exposition of the theory of measure and integration. It is intendend for students, and also as a reference work. The body of the text can be read by a student with a firm background in analysis, whereas the supplements treat more advanced topics, and require somewhat more maturity. Although the results given here are the standard ones, the authors have taken a new approach, systematically exploiting the concepts of -ring and -simplicity.

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[目次]

  • 0: Preliminaries.- Sets.- Functions.- Countability.- Orderings and Lattices.- Convergence in ?*.- Unordered Summability.- Hausdorff Maximal Principle.- 1: Pre-Measures.- Supplement: Contents.- Supplement: G Invariant Contents.- Supplement: Caratheodory Pre-Measures.- 2: Pre-Measure to Pre-Integral.- Supplement: Volume ?n
  • The Iterated Integral.- Supplement: Pre-Integrals on Cc(X) and C0(X).- 3: Pre-Integral to Integral.- 4: Integral to Measure.- Supplement: Lebesgue Measure ?n for ?n.- Supplement: Measures on B?(X).- Supplement: G Invariant Measures.- 5: Measurability and ?-Simplicity.- Supplement: Standard Borel Spaces.- 6: The Integral I? on L1(?).- Supplement: Borel Measures and Positive Functionals.- 7: Integrals* and Products.- Supplement: Borel Product Measure.- 8: Measures* and Mappings.- Supplement: Stieltjes Integration.- Supplement: The Image of ?p Under a Smooth Map 100 Supplement: Maps of Borel Measures*
  • Convolution.- 9: Signed Measures and Indefinite Integrals.- Supplement: Decomposable Measures.- Supplement: Haar Measure.- 10: Banach Spaces.- Supplement: The Spaces C0(X)* and L1(?)*.- Supplement: Complex Integral and Complex Measure.- Supplement: The Bochner Integral.- Selected References.

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この本の情報

書名 Measure and integral
著作者等 Kelley, John L.
Srinivasan, T. P.
シリーズ名 Graduate texts in mathematics
巻冊次 v. 1
出版元 Springer-Verlag
刊行年月 c1988
ページ数 x, 150 p.
大きさ 25 cm
ISBN 3540966331
0387966331
NCID BA01420876
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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