Notes

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 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.

Classification

• LCC: QA312
• Dewey Decimal: 515/.43

Book Details

• Language: eng
• Physical Description: xiv, 202 p. : ill. ; 22 cm.
• Edition Info: (alk. paper)

Subjects

• Professional & Technical -- Professional Science -- Mathematics -- Geometry & Topology -- Topology
• Professional & Technical -- Professional Science -- Mathematics -- Pure Mathematics -- Calculus
• Science -- Mathematics -- Geometry & Topology -- General Geometry
• Science -- Mathematics -- Pure Mathematics -- Calculus
• Lebesgue integral

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