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Abstract: We study Borel systems and continuous systems of measures, with a focus onmapping properties: compositions, liftings, fibred products and disintegration.Parts of the theory we develop can be derived from known work in theliterature, and in that sense this paper is of expository nature. However, weput the above notions in the spotlight and provide a self-contained, purelymeasure-theoretic, detailed and thorough investigation of their properties, andin that aspect our paper enhances and complements the existing literature. Ourwork constitutes part of the necessary theoretical framework for categoricalconstructions involving measured and topological groupoids with Haar systems, aline of research we pursue in separate papers.



Author: Aviv Censor, Daniele Grandini

Source: https://arxiv.org/







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