| Document Type
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BL
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| Record Number
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587164
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| Doc. No
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b416383
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| Main Entry
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Franks, John M.,1943-
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| Title & Author
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A (terse) introduction to Lebesgue integration /\ John Franks
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| Publication Statement
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Providence, R.I. :: American Mathematical Society,, c2009
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| Series Statement
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Student mathematical library ;; v. 48
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| Page. NO
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xiv, 202 p. :: ill. ;; 22 cm
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| ISBN
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9780821848623 (alk. paper)
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: 0821848623 (alk. paper)
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| Bibliographies/Indexes
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Includes bibliographical references (p. 197) and index
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| Contents
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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
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| Subject
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Lebesgue integral
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| Dewey Classification
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515/.43
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| LC Classification
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QA312.F698 2009
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QA312.F698 2009
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| Parallel Title
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Terse introduction to Lebesgue integration
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: Introduction to Lebesgue integration
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