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A brief review of Radon-Nikodýmification

Thierry De Pauw

Abstract

We review recent results on Radon-Nikodýmification of abstract measure spaces, the particular case of integral geometric measure, and applications to the dual of SBV.

A brief review of Radon-Nikodýmification

Abstract

We review recent results on Radon-Nikodýmification of abstract measure spaces, the particular case of integral geometric measure, and applications to the dual of SBV.
Paper Structure (7 sections, 9 theorems, 17 equations, 1 table)

This paper contains 7 sections, 9 theorems, 17 equations, 1 table.

Table of Contents

  1. Foreword
  2. Motivation
  3. Injectivity and surjectivity of the canonical map $\mathbf{L}_\infty \to \mathbf{L}_1^*$
  4. Measurable spaces with negligibles
  5. Integral geometric measure
  6. The dual of $\mathbf{SBV}$
  7. Acknowledgements

Key Result

Theorem 1

For any measure space $(X,\mathscr{A},\mu)$, the map $\Upsilon$ (recall eq.100) is surjective if and only if the measurable space with negligibles $\left(X,\mathscr{A}, \mathscr{N}_{\mu,\mathop{\mathrm{\mathrm{loc}}}\nolimits}\right)$ is localizable.

Theorems & Definitions (9)

  • Theorem
  • Theorem
  • Theorem
  • Theorem
  • Theorem
  • Theorem
  • Theorem
  • Theorem
  • Theorem