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Books, Free Shipping, Lebesgue Integration On Euclidean Space Revised Edition

Posted at: Offers to Sell and Export | Posted on: Fri 16 Jul, 2010 9:10 am | Product Category: Reference books [3760]
 
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Product Description:

Contents:


Preface

Bibliography

Acknowledgments

1 Introduction to Rn

A Sets

B

Countable Sets

C Topology

D Compact Sets

E Continuity

F The Distance Function

2 Lebesgue Measure on Rn

A Construction

B Properties of Lebesgue Measure

C Appendix: Proof of P1 and P2

3 Invariance of Lebesgue Measure

A Some Linear Algebra

B Translation and Dilation

C Orthogonal Matrices

D The General Matrix

4 Some Interesting Sets

A A Nonmeasurable Set

B A Bevy of Cantor Sets

C The Lebesgue Function

D Appendix: The Modulus of Continuity of the Lebesgue Functions

5 Algebras of Sets and Measurable Functions

A Algebras and a-Algebras

B Borel Sets

C A Measurable Set which Is Not a Borel Set

D Measurable Functions

E Simple Functions

6 Integration

A Nonnegative Functions

B General Measurable Functions

C Almost Everywhere

D Integration Over Subsets of Rn

E Generalization: Measure Spaces

F Some Calculations

G Miscellany

7 Lebesgue Integral on Rn

A Riemann Integral

B Linear Change of Variables

C Approximation of Functions in L1

D Continuity of Translation in L1

8 Fubini's Theorem for Rn

9 The Gamma Function

A Definition and Simple Properties

B Generalization

C The Measure of Balls

D Further Properties of the Gamma Function

E Stirling's Formula

F The Gamma Function on R

10 LP Spaces, A Definition and Basic Inequalities

B Metric Spaces and Normed Spaces

C Completeness of Lp

D The Case p=∞

E Relations between Lp Spaces

F Approximation by C∞c (Rn)

G Miscellaneous Problems ;

H The Case 0[p[1

11 Products of Abstract Measures

A Products of 5-Algebras

B Monotone Classes

C Construction of the Product Measure

D The Fubini Theorem

E The Generalized Minkowski Inequality

12 Convolutions

A Formal Properties

B Basic Inequalities

C Approximate Identities

13 Fourier Transform on Rn

A Fourier Transform of Functions in L1 (Rn)

B The Inversion Theorem

C The Schwartz Class

D The Fourier-Plancherel Transform

E Hilbert Space

F Formal Application to Differential Equations

G Bessel Functions

H Special Results for n = i

I Hermite Polynomials

14 Fourier Series in One Variable

A Periodic Functions

B Trigonometric Series

C Fourier Coefficients

D Convergence of Fourier Series

E Summability of Fourier Series

F A Counterexample

G Parseval's Identity

H Poisson Summation Formula

I A Special Class of Sine Series

15 Differentiation

A The Vitali Covering Theorem

B The Hardy-Littlewood Maximal Function

C Lebesgue's Differentiation Theorem

D The Lebesgue Set of a Function

E Points of Density

F Applications

G The Vitali Covering Theorem (Again)

H The Besicovitch Covering Theorem

I The Lebesgue Set of Order p

J Change of Variables

K Noninvertible Mappings

16 Differentiation for Functions on R

A Monotone Functions

B Jump Functions

C Another Theorem of Fubini

D Bounded Variation

E Absolute Continuity

F Further Discussion of Absolute Continuity

G Arc Length

H Nowhere Differentiable Functions

I Convex Functions

Index

Symbol Index

Product Details

Author Frank Jones

Publisher World Publishing Corporation

Isbn 9787510005558

Published January 2010

Pages 588

Size 24k

Edition First

Format Paperback

Language English

Page material gelatine plate paper



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