The Bochner-Radon-Nikodym theory for vector-valued measures

In this paper, we investigate the vector-valued measures, absolutely continuous measures, and the Bochner-Radon-Nikodym property for Banach spaces. These types of studies have a plethora of applications in stochastic processes, representation theory, and recently in neural nets. We establish the necessary and sufficient conditions that Banach space possesses the Radon-Nikodym property.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-01-15
DOI
https://doi.org/10.5281/zenodo.14776043
Primary Topic
Advanced Banach Space Theory
Type
article
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article

The Bochner-Radon-Nikodym theory for vector-valued measures

Zenodo (CERN European Organization for Nuclear Research)
Advanced Banach Space Theory
article

The Bochner-Radon-Nikodym theory for vector-valued measures

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Abstract

In this paper, we investigate the vector-valued measures, absolutely continuous measures, and the Bochner-Radon-Nikodym property for Banach spaces. These types of studies have a plethora of applications in stochastic processes, representation theory, and recently in neural nets. We establish the necessary and sufficient conditions that Banach space possesses the Radon-Nikodym property.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 49%
Advanced Banach Space Theory
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The Bochner-Radon-Nikodym theory for vector-valued measures · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS