What question did this study set out to answer?

The aim is to examine normed spaces of measurable mappings and their relationship to bounded measures.

March 21, 2026Proceedings of the Steklov Institute of Mathematics2 citations

Integration of Functions with Values in Spaces of Measures

MAMiloš ArsenovićBryansk State University VBVladimir Igorevich BogachevNational Research University Higher School of Economics MKMihailo KrstićUniversity of Nis

Key Points

The aim is to examine normed spaces of measurable mappings and their relationship to bounded measures.
Analysis of measurable mappings in various normed spaces.
Definition through setwise integrability and Kantorovich–Rubinshtein norms.
Comparison with classical spaces of Bochner integrable mappings.
Identification of spaces that are larger than classical Bochner integrable mappings.
Demonstration of connections to disintegrations of measures.
Establishment of new frameworks for analyzing integrability.

Abstract

We study several normed spaces of measurable mappings with values in spaces of bounded measures. Such spaces of mappings arise naturally in connection with disintegrations of measures and are larger than the classical space of Bochner integrable mappings. They are defined by means of setwise integrability or by means of Kantorovich–Rubinshtein-type norms.

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