عنوان

A (terse) introduction to Lebesgue integration /

0821848623 (alk. paper)

9780821848623 (alk. paper)

b416383

A (terse) introduction to Lebesgue integration /

[Book]

John Franks

Providence, R.I. :

American Mathematical Society,

c2009

xiv, 202 p. :

ill. ;

22 cm

Student mathematical library ;

v. 48

Includes bibliographical references (p. 197) and index

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 -- 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

0

Terse introduction to Lebesgue integration

Introduction to Lebesgue integration

Lebesgue integral

Franks, John M.,1943-

20100405132355.0

[Book]

Y