On the existence of invariant measures that behave like area

Baldwin, Stewart

doi:10.1090/S0002-9939-1992-1112485-1

On the existence of invariant measures that behave like area
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by Stewart Baldwin

Proc. Amer. Math. Soc. 115 (1992), 89-96

DOI: https://doi.org/10.1090/S0002-9939-1992-1112485-1

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Abstract:

A countably additive measure on a locally compact, separable, metric space $X$ will be called area-like if points have measure zero, compact sets have finite measure, and nonempty open sets have nonzero measure. Given a homeomorphism $f$ of $X$, we examine criteria that guarantee the existence or nonexistence of arealike measures that are invariant under $f$.

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