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- W1562967287 abstract "Let $X$ and $Y$ be metric spaces. We show that the tight images of a (fixed) tight Borel probability measure $mu$ on $X$, under all Borel mappings $fcolon Xto Y$, form a closed set in the space of tight Borel probability measures on $Y$ with the weak$^*$-topology. In contrast, the set of images of $mu$ under all continuous mappings from $X$ to $Y$ may not be closed. We also characterize completely the set of tight images of $mu$ under Borel mappings. For example, if $mu$ is non-atomic, then all tight Borel probability measures on $Y$ can be obtained as images of $mu$, and as a matter of fact, one can always choose the corresponding Borel mapping to be of Baire class 2." @default.
- W1562967287 created "2016-06-24" @default.
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- W1562967287 date "2002-03-29" @default.
- W1562967287 modified "2023-10-14" @default.
- W1562967287 title "On images of Borel measures under Borel mappings" @default.
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- W1562967287 doi "https://doi.org/10.1090/s0002-9939-02-06434-1" @default.
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