Absolute continuity and uniqueness of measures on metric spaces

Mattila, Pertti

doi:10.1090/S0002-9947-1981-0613793-8

Absolute continuity and uniqueness of measures on metric spaces
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Trans. Amer. Math. Soc. 266 (1981), 233-242 Request permission

Abstract:

We show that if two Borel regular measures on a separable metric space are in a suitable sense homogeneous, then they are mutually absolutely continuous. We use such absolute continuity theorems together with some density theorems to prove the uniqueness of measures more general than Haar measures.

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