Advertisement

Modes of Convergence

  • Rinaldo B. Schinazi
Chapter
  • 841 Downloads

Abstract

Let \((X,\mathcal {M},\mu )\) be a measure space. Consider L1(μ) the space of integrable functions and let
$$\displaystyle d(f,g)=\int |f-g|d\mu . $$
For all f, g, and h in L1(μ) it is easy to check that d(f, g) ≥ 0, d(f, g) = d(g, f), and
$$\displaystyle d(f,g)\leq d(f,h)+d(h,g). $$

References

  1. W. Rudin, Real and Complex Analysis, 3rd edn. (McGraw Hill, New York, 1987)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Rinaldo B. Schinazi
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoColorado SpringsUSA

Personalised recommendations