Radon-Nikodýmification of arbitrary measure spaces

• P. Bouafia ^[1] ; Thierry De Pauw ^[2]
  1. [1] Fédération de Mathématiques FR3487, CentraleSupélec 3 rue Joliot Curie, 91190 Gif-sur-Yvette, France
  2. [2] Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013, Paris, France
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 38, Nº 2, 2023, págs. 139-203
• Idioma: inglés
• DOI: 10.17398/2605-5686.38.2.139
• Enlaces
  • Texto completo  1    2  
• Resumen

  • We study measurable spaces equipped with a σ-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version – a kind of fiber space that locally describes their directions – defined by a universal property in an appropriate category that we introduce. These methods allow to promote each measure space (X, A , µ) to a strictly localizable version (X̂, Â, µ̂), so that the dual of L1 (X, A , µ) is L∞ (X̂, Â, µ̂). Corresponding to this duality is a generalized Radon-Nikodým theorem. We also provide a characterization of the strictly localizable version in special cases that include integral geometric measures, when the negligibles are the purely unrectifiable sets in a given dimension.

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