عنوان

A (terse) introduction to Lebesgue integration /

شابک

0821848623 (alk. paper)

شابک

9780821848623 (alk. paper)

شماره

b416383

عنوان اصلي

A (terse) introduction to Lebesgue integration /

نام عام مواد

[Book]

نام نخستين پديدآور

John Franks

محل نشرو پخش و غیره

Providence, R.I. :

نام ناشر، پخش کننده و غيره

American Mathematical Society,

تاریخ نشرو بخش و غیره

c2009

نام خاص و کميت اثر

xiv, 202 p. :

ساير جزييات

ill. ;

ابعاد

22 cm

عنوان فروست

Student mathematical library ;

مشخصه جلد

v. 48

متن يادداشت

Includes bibliographical references (p. 197) and index

متن يادداشت

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

بدون عنوان

0

عنوان اصلي به زبان ديگر

Terse introduction to Lebesgue integration

عنوان اصلي به زبان ديگر

Introduction to Lebesgue integration

موضوع مستند نشده

Lebesgue integral

شماره

ويراست

شماره رده

شماره رده

نشانه اثر

نشانه اثر

مستند نام اشخاص تاييد نشده

Franks, John M.,1943-

تاريخ عمليات

20100405132355.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y