The translation invariant product measure problem in non-sigma finite case

2023/08/15 by Nicha Khenkhok, Khenkhok, Nicha
Computer Science · Mathematics · #28A35 28A35 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Approximation and Integration #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2309.17247

openalex publication_date 2023/08/15 · openalex created_date 2023/10/03 · openalex updated_date 2026/07/28

Abstract

We give an example of non-translation invariant product measure obtained from two translation invariant measures, one of which is non-sigma finite. This particular example also suggests that there can be infinitely many product measures if we abandon the sigma-finiteness assumption.

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