Measure Theory

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Measure theory is that branch of real analysis which investigates σ-algebras, measures, measurable functions and integrals.

Chapters[edit]

  1. Basic Structures And Definitions 0% developed  as of Jul 12, 2006 (Jul 12, 2006)
    1. Semialgebras, Algebras and σ-algebras 25% developed  as of Jul 12, 2006 (Jul 12, 2006)
    2. Measures 25% developed  as of Dec 16, 2012 (Dec 16, 2012)
    3. Measurable Functions 0% developed  as of Dec 16, 2012 (Dec 16, 2012)
    4. Extension of a Measure 0% developed  as of Jul 12, 2006 (Jul 12, 2006)
    5. Completion of Measure Spaces 0% developed  as of Jul 12, 2006 (Jul 12, 2006)
    6. Regular Measures 0% developed  as of Jul 12, 2006 (Jul 12, 2006)
  2. Integration 50% developed  as of Nov 3, 2008 (Nov 3, 2008)
  3. Riesz' representation theorem
  4. L^p spaces

Contents[edit]

  1. Advanced set theory
  2. Algebras and σ-algebras
  3. Pre-measures and measures
  4. Theorems on measures
  5. Multiplicative systems, Dynkin systems
  6. Carathéodory's theorem and extension of pre-measures
  7. Measurable functions, Lebesgue integration
  8. Theorems on Lebesgue integrals (note to self: don't forget trafo of vars, leibniz integral rule)
  9. Lp spaces
  10. Riesz representation theorem, Radon–Nikodym theorem

References[edit]

  • Bartle, Robert Gardner. The Elements of Integration and Lebesgue Measure. Wiley, 1995. 192 p. ISBN 0471042226
  • DiBenedetto, Emmanuele. Real Analysis. Springer, 2002. 420 p. ISBN 0817642315
  • Folland, Gerald B.. Real Analysis: Modern Techniques and Their Applications. 2.ed. 1999. 408 p. ISBN 0471317160
  • Halmos, Paul Richard. Measure Theory. Springer, 1974. ISBN 0387900888
  • Munroe, Marshall Evans. Introduction to Measure and Integration. 2.ed. Addison-Wesley, 1959. 310 p.
  • Royden, M.. Real Analysis. New York: Collier Macmillan, 1988. ISBN 0024041513
  • W. Rudin, Real and Complex analysis, 3.ed. McGraw-Hill International (1987). 430 p. ISBN 0070542341
  • Lang, Serge. Analysis I. 3.ed. Addison-Wesley, 1973. 460 p.
  • Tao, Terence: An introduction to measure theory

Users Actively Contributing[edit]

  • Bunder :
    • At the moment, before making any writing of material i'm creating a sort of workflow by using templates
  • Raliaga :
    • I'm adding content to the first section of the first chapter, including some insights about the "reason of being" of the definitions and comments on the importance of the propositions presented.
  • SPat talk :
    • Basically uploading my lecture notes.