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Real Analysis pp 221-274 | Cite as

The Lp(E) Spaces

  • Emmanuele DiBenedetto
Part of the Birkhäuser Advanced Texts book series (BAT)

Abstract

Let { X,A,μ} be a measure space and let E be a measurable subset of X. A measurable function \(f:E \to {{\mathbb{R}}^{*}}\) is said to be in L P (E) for P≥1 if is integrable on E, i.e., if
$$ \left\| f \right\|_p \mathop = \limits^{def} \left( {\smallint _E \left| f \right|^p d\mu } \right)^{1/p} < \infty $$
(1.1)p

Keywords

Weak Convergence Simple Function Cauchy Sequence Measurable Subset Finite Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Emmanuele DiBenedetto
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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