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001 ocn306803455;

003 OCoLC;

005 20141212045525.0;

008 090213s2009 riua b 001 0 eng ;

010 a| 2009005870;

020 a| 9780821848623 (alk. paper);

020 a| 0821848623 (alk. paper);

029 1 a| AU@b| 000043849970;

029 1 a| BWXb| R8796886;

035 a| (Sirsi) o306803455;

035 a| (OCoLC)306803455;

049 a| EREE;

050 00 a| QA312b| .F698 2009;

082 00 a| 515/.432| 22;

100 1 a| Franks, John M.,d| 1943-=| ^A1006994;

245 12 a| A (terse) introduction to Lebesgue integration /c| John Franks.;

246 3 a| Terse introduction to Lebesgue integration;

246 30 a| Introduction to Lebesgue integration;

300 a| xiv, 202 pages :b| illustrations ;c| 22 cm.;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

490 1 a| Student mathematical library ;v| v. 48;

504 a| Includes bibliographical references (p. 197) and index.;

505 0 a| 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.;

650 0 a| Lebesgue integral.=| ^A360991;

830 0 a| Student mathematical library ;v| v.48.=| ^A438915;

856 41 3| Table of contents onlyu| http://www.loc.gov/catdir/toc/fy1002/2009005870.html;

949 a| QA312 .F698 2009h| JOYNER48i| 30372015233080o| jcmt;

994 a| C0b| ERE;

938 a| YBP Library Servicesb| YANKn| 2990063;

938 a| Blackwell Book Serviceb| BBUSn| R8796886c| $37.00;

596 a| 1;

998 a| 2178215;

999 a| QA312 .F698 2009w| LCc| 1i| 30372015233080d| 4/4/2013e| 4/5/2010f| 4/4/2013g| 1l| JGESm| JOYNERn| 1r| Ys| Yt| JGESBKu| 2/16/2010x| BOOKz| JSTACKSo| .STAFF. jcmt;

A (terse) introduction to Lebesgue integration / John Franks.

Author/creator	Franks, John M., 1943-
Format	Book
Publication Info	Providence, R.I. : American Mathematical Society, ©2009.
Description	xiv, 202 pages : illustrations ; 22 cm.
Supplemental Content	Table of contents only
Subjects	Lebesgue integral.

Variant title	Terse introduction to Lebesgue integration
Portion of title	Introduction to Lebesgue integration
Series	Student mathematical library ; v. 48 Student mathematical library ; v.48. ^A438915
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 -- 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.
Bibliography note	Includes bibliographical references (p. 197) and index.
LCCN	2009005870
ISBN	9780821848623 (alk. paper)
ISBN	0821848623 (alk. paper)

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A (terse) introduction to Lebesgue integration / John Franks.

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