Published by John Wiley & Sons A Halsted Press Book, 1986. This book provides a basic course in Lebesgue Measure, gives detailed explanations of reasons of work and methods used together with explicitly in an easy, lucid style. A very effective learning text.
Author(s): P. K Jain, V. P. Gupta
Edition: 1st
Publisher: Wiley / Halsted Press
Year: 1986
Language: English
Pages: C, x, 260, B
I Preliminaries
1 Set And Set Inclusion
2 Functions
3 Supremum And Infimum
4 Intervals
5 Open, Closed .and Perfect Sets
6 Sequences And Series
7 Continuity And Differentiability
II Infinite Sets
1 Equivalent Sets
2 Finite And Infinite Sets
3 Countable Sets
4 Uncountable Sets
5 Cardin.ality Of Sets
6 Order Relation In Cardinal Numbers
7 Addmon Of Cardinal Numbers
8 Multiplication Of Cardinal Numbers
9 Exponentiation Of Cardinal Numbers
10 Cantor-like Sets
III Measurable Sets
1 Length Of Sets
2 Outer Measure
3 Lebesgue Measure
4 Properties Of Measurable Sets
5 Borel Sets And Their Measurability
6 Further Properties Of Measurable Sets
7 Characterizations Of Measurable Sets
8 Nonmeasurable Sets
IV Measurable Functions
1 Definition
2 Properties Of Measurable Funcdons
3 Step Function
4 Operations On Measurable Funci'ions
5 Characteristic Funcfion
6 Simple Function
7 Continuous Funcfion
8 Sets Of Measure Zero
9. Borel Measurable Funcfion
10 Sequence Of Functions
11 The Structure Of Measurable Funcllons
12. Convergence In Measure
V Lebesgue Integral
1 Riemann Integral
2 Lebesgue Integral of A Bounded Funci'ion
3 Comparison of Riemann Integral and Lebesgue Integral
4 Properties of The Lebesgue Integral for Bounded Measurable Funct.ions
5 Integral of Nonnegative Measurable Functions
6 General Lebesgue Integral
7 Improper Integrals
VI Differentiation And Integration
1 Dini Derivatives
2 Differentiation of Monotone Functions
3 Functions of Bounded Variation
4 Differentiation of an Integral
5 Lebesgue Sets
6 Absolutely Continuous Functions
7 Integral of The Derivative
VII The Lebesgue L^p Spaces
1 Notion Of Banach Spaces
2 The Classes L^p
3 The Holder and Minkowski Inequalities
4 L^p Banach Spaces
5 Convergence in The Mean
6 Properties of L^p Spaces
7 Bounded Linear Functionals On L^p Spaces
Appendix I: Existence Of Riemann Integral
Appendix II: Nowhere Differentiable Continuous Functions
Appendix III: The Development Of The Notion Of The Integral
Bibliography
List of Symbols and Notations
Index
Back Cover
