A Note on Lusin measurability in measure spaces

Year, pages: 2003, 273 - 290

If $X$ and $Y$ are Hausdorff topological spaces, $\Bbb P(X)$ and $\Bbb P(Y)$ the corresponding spaces of Radon probability measures, then any universally Lusin measurable map $f:X\to Y$ defines ``the image measure map'' $\tilde f:\Bbb P(X)\to\Bbb P(Y)$. We ask and partially provide answers to the following problems: \roster \item When the surjectivity of $f$ implies the surjectivity of $\tilde f$? \item Under which circumstances is the map $\tilde f$ universally Lusin measurable? \endroster It is a known fact that both problems are answered positively if $X$ and $Y$ are Souslin spaces. Our results show that the desired properties are connected more generally with the presence or absence of the measure convexity of the spaces $\Bbb P(X)$ and $\Bbb P(Y)$.

Štěpán, J. 2003. A Note on Lusin measurability in measure spaces. In Mathematica Slovaca, vol. 53, no.3, pp. 273-290. 0139-9918.

Štěpán, J. (2003). A Note on Lusin measurability in measure spaces. Mathematica Slovaca, 53(3), 273-290. 0139-9918.