A characterization of maps of bounded compression
Dello Schiavo L. 2024. A characterization of maps of bounded compression. Mathematical Communications. 29(1), 137–142.
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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 corrobo-rates the assertion that maps of bounded deformation are a natural class of morphisms for the category of complete and separable metric measure spaces.
Publishing Year
Date Published
2024-01-01
Journal Title
Mathematical Communications
Acknowledgement
The author gratefully acknowledges funding of his current position by the Austrian Science
Fund (FWF), grant ESPRIT208. He is grateful to Enrico Pasqualetto for pointing out some
references on maps of bounded compression.
Volume
29
Issue
1
Page
137-142
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eISSN
IST-REx-ID
Cite this
Dello Schiavo L. A characterization of maps of bounded compression. Mathematical Communications. 2024;29(1):137-142.
Dello Schiavo, L. (2024). A characterization of maps of bounded compression. Mathematical Communications. Udruga Matematicara Osijek.
Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.” Mathematical Communications. Udruga Matematicara Osijek, 2024.
L. Dello Schiavo, “A characterization of maps of bounded compression,” Mathematical Communications, vol. 29, no. 1. Udruga Matematicara Osijek, pp. 137–142, 2024.
Dello Schiavo L. 2024. A characterization of maps of bounded compression. Mathematical Communications. 29(1), 137–142.
Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.” Mathematical Communications, vol. 29, no. 1, Udruga Matematicara Osijek, 2024, pp. 137–42.
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