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A (terse) introduction to Lebesgue integration

Author: John M Franks
Publisher: Providence, R.I. : American Mathematical Society, ©2009.
Series: Student mathematical library, v. 48.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Provides a student's first encounter with the concepts of measure theory and functional analysis. This book reflects the belief that difficult concepts should be introduced in their simplest and most  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: John M Franks
ISBN: 9780821848623 0821848623
OCLC Number: 306803455
Description: xiv, 202 pages : illustrations ; 22 cm.
Contents: The regulated and Riemann integrals --
Introduction --
Basic properties of an integral --
Step functions --
Uniform and pointwise convergence --
Regulated integral --
The fundamental theorem of calculus --
The Riemann integral --
Lebesgue measure --
Introduction --
Null sets --
Sigma algebras --
Lebesgue Measure --
The Lebesgue density theorem --
Lebesgue measurable sets --
Summary --
The Lebesgue integral --
Measurable functions --
The Lebesgue integral of bounded functions --
The bounded convergence theorem --
The integral of unbounded functions --
Non-negative functions --
Convergence theorems --
Other measures --
General measurable functions --
The Hilbert space L² --
Square integrable functions --
Convergence in L² --
Hilbert space --
Fourier series --
Complex Hilbert space --
Classical Fourier series --
Real Fourier series --
Integrable complex-valued functions --
The complex Hilbert space L²c [pi, pi] --
The Hilbert Space L²c[T] --
Two ergodic transformations --
Measure preserving transformations --
Ergodicity --
The Birkhoff ergodic theorem --
Appendix A. Background and foundations --
The completeness of R --
Functions and sequences --
Limits --
Complex limits --
Set theory and countability --
Open and closed sets --
Compact subsets of R --
Continuous and differentiable functions --
Real vector spaces --
Complex vector spaces --
Complete normed vector spaces --
Appendix B. Lebesgue measure --Introduction --
Outer measure --
The o-algebra of Lebesgue measurable sets --
The existence of Lebesgue measure --
Appendix C.A non-measurable set.
Series Title: Student mathematical library, v. 48.
Other Titles: Introduction to Lebesgue integration
Responsibility: John Franks.
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