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  • Corneliu Constantinescu
  • Wolfgang Filter
  • Karl Weber
  • Alexia Sontag
Chapter
  • 674 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 454)

Abstract

For (X, ℜ, μ) a positive measure space, it has already been noted that μ - a.e. equality is an equivalence relation, and the relation ≤ μ-a.e. a preorder, on.This section studies the structure of the equivalence classes into which μ-a,e. equality partitions.Since the set X/X( ℜ) is always u-null (2.7.7 a)), only the function values on the set X(ℜ) have any significance when equivalence classes are formed: whether we form equivalence classes by partitioning or by partitioningX(ℜ) the resulting structures will be isomorphic. Nevertheless, it is natural to allow functions on an arbitrary XX(ℜ). Our choice is to form μ-equivalence classes by partitioning the set X(ℜ). For arbitrary XX(ℜ), we then associate to f ∈ the μ-equivalence class determined by the restriction of f to X(ℜ). This choice simplifies matters somewhat when we work with different sets at the same time.

Keywords

Vector Lattice Finite Subset Order Topology Countable Subset Minkowski Inequality 
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 1998

Authors and Affiliations

  • Corneliu Constantinescu
    • 1
  • Wolfgang Filter
    • 2
  • Karl Weber
    • 3
  • Alexia Sontag
    • 4
  1. 1.Department of MathematicsETH-ZürichZürichSwitzerland
  2. 2.Department of Mathematics, Faculty of EngineeringUniversità di PalermoPalermoItaly
  3. 3.Technikum WinterthurWinterthurSwitzerland
  4. 4.Department of MathematicsWellesley CollegeWellesleyUSA

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