A Characterization of Maps of Bounded Compression

Lorenzo Dello Schiavo

Vol. 29 No. 1 (2024)

Regular Articles

A Characterization of Maps of Bounded Compression

Published 2024-03-12

Lorenzo Dello Schiavo

Lorenzo Dello Schiavo
Institute of Science and Technology Austria

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Abstract

A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of maps of bounded compression/deformation by means of the measure-algebra functor and corroborates the assertion that maps of bounded deformation are the natural class of morphisms for the category of complete and separable metric measure spaces.

Keywords

maps of bounded compression, maps of bounded deformation, measure algebras

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Supplementary File(s)

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