In: Tatra Mountains Mathematical Publications, vol. 65, no. 1
Adam Paszkiewicz - Elżbieta Wagner-Bojakowska
Detaily:
Rok, strany: 2016, 143 - 149
Kľúčové slová:
sets of Lebesgue measure zero, sets of the first category, microscopic sets on the plane, Fubini Theorem, Fubini property
O článku:
In 2000, I. Rec\l aw and P. Zakrzewski introduced the notion of Fubini Property for the pair ($\I,\J)$ of two $sigma$-ideals in the following way. Let $\I$ and $\J$ be two $\sigma$-ideals on Polish spaces $X$ and $Y$, respectively.
The pair $(\I,\J)$ has the Fubini Property (FP) if for every Borel subset $B$ of $X\times Y$ such that all its vertical sections $B_x=\bl\{y\in Y: (x,y)\in B\br\}$ are in $\J$, then the set of all $y\in Y$,
for which horizontal section $B^y=\bl\{x\in X: (x,y)\in B\br\}$ does not belong to $\I$, is a set from~$\J$, i.e.,
$$
\{y\in Y\!: B^y\not\in\I\}\in\J.
$$
\par
The Fubini property for the $\sigma$-ideal $\M$ of microscopic sets is considered
and the proof that the pair $(\M,\M)$ does not satisfy (FP) is given.
Ako citovať:
ISO 690:
Paszkiewicz, A., Wagner-Bojakowska, E. 2016. Fubini property for microscopic sets. In Tatra Mountains Mathematical Publications, vol. 65, no.1, pp. 143-149. 1210-3195.
APA:
Paszkiewicz, A., Wagner-Bojakowska, E. (2016). Fubini property for microscopic sets. Tatra Mountains Mathematical Publications, 65(1), 143-149. 1210-3195.