## Illinois Journal of Mathematics

### On compactness of measures on Polish spaces

#### Abstract

We present some results related to the question whether every finite measure $\mu$ defined on a $\sigma$--algebra $\Sigma\sub \Borel[0,1]$ is countably compact. In particular, we show that for every finite measure space $(X,\Sigma,\mu)$, where $X$ is a Polish space and $\Sigma\sub \Borel(X)$, there is a regularly monocompact measure space $(\widehat{X},\widehat{\Sigma},\widehat{\mu})$ and an inverse-measure-preserving function $f:\widehat{X}\to X$.

#### Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 531-545.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138033

Digital Object Identifier
doi:10.1215/ijm/1258138033

Mathematical Reviews number (MathSciNet)
MR2164351

Zentralblatt MATH identifier
1085.28008

#### Citation

Borodulin-Nadzieja, Piotr; Plebanek, Grzegorz. On compactness of measures on Polish spaces. Illinois J. Math. 49 (2005), no. 2, 531--545. doi:10.1215/ijm/1258138033. https://projecteuclid.org/euclid.ijm/1258138033