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2 results

  • 2 - Lebesgue Integral

  • from PART I - Measure And Integration
  • Martin Buntinas, Loyola University, Chicago
  • Book:
    Classical and Discrete Functional Analysis with Measure Theory
    Published online:
    06 January 2022
    Print publication:
    20 January 2022, pp 97-117

  • Summary

    This chapter starts with definitions and basic properties of Measurable Functions. The Lebesgue Integral is systematically developed; first for Simple Functions, then for Nonnegative Functions, and finally for the General Case. Egorov's Theorem is proven. The important Lebesgue Limit Theorems that distinguish Lebesgue Integration from Riemann and Stieltjes Integration are discussed and proven.

  • SOME REVERSES OF THE JENSEN INEQUALITY WITH APPLICATIONS

  • S. S. DRAGOMIR
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 87 / Issue 2 / April 2013
    Published online by Cambridge University Press:
    07 February 2013, pp. 177-194
    Print publication:
    April 2013
    • Article
      • You have access
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  • Two new reverses of the celebrated Jensen’s inequality for convex functions in the general setting of the Lebesgue integral, with applications to means, Hölder’s inequality and $f$-divergence measures in information theory, are given.