This exploration investigates measurable mappings in normed spaces, suggesting new avenues for integrating functions.
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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Arsenović et al. (2025) studied this question.
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