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http://hdl.handle.net/10662/19479
Title: | Radon-Nikodýmification of arbitrary measure spaces |
Authors: | Bouafia, P. De Pauw, T. |
Keywords: | Measurable space with negligibles;Radon-Nikodým Theorem;Strictly localizable measure space;Integral geometric measure;Purely unrectifiable |
Issue Date: | 2023 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | 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-Nikoým 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 unrecti_able sets in a given dimensión. |
URI: | http://hdl.handle.net/10662/19479 |
ISSN: | 0213-8743 |
DOI: | 10.17398/2605-5686.38.2.125 |
Appears in Collections: | Extracta Mathematicae Vol. 38, nº 2 (2023) |
Files in This Item:
File | Description | Size | Format | |
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2605-5686_38_2_139.pdf | 724,62 kB | Adobe PDF | View/Open |
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