On nonmeasurable images

Rałowski, Robert, and Żeberski, Szymon. "On nonmeasurable images." Czechoslovak Mathematical Journal 60.2 (2010): 423-434. <http://eudml.org/doc/38017>.

@article{Rałowski2010,
abstract = {Let $(X,\mathbb \{I\})$ be a Polish ideal space and let $T$ be any set. We show that under some conditions on a relation $R\subseteq T^2\times X$ it is possible to find a set $A\subseteq T$ such that $R(A^2)$ is completely $\mathbb \{I\} $-nonmeasurable, i.e, it is $\mathbb \{I\}$-nonmeasurable in every positive Borel set. We also obtain such a set $A\subseteq T$ simultaneously for continuum many relations $(R_\alpha )_\{\alpha <2^\omega \}.$ Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.},
author = {Rałowski, Robert, Żeberski, Szymon},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonmeasurable set; Bernstein set; Polish ideal space; nonmeasurable set; Bernstein set; Polish ideal space},
language = {eng},
number = {2},
pages = {423-434},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On nonmeasurable images},
url = {http://eudml.org/doc/38017},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Rałowski, Robert
AU - Żeberski, Szymon
TI - On nonmeasurable images
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 423
EP - 434
AB - Let $(X,\mathbb {I})$ be a Polish ideal space and let $T$ be any set. We show that under some conditions on a relation $R\subseteq T^2\times X$ it is possible to find a set $A\subseteq T$ such that $R(A^2)$ is completely $\mathbb {I} $-nonmeasurable, i.e, it is $\mathbb {I}$-nonmeasurable in every positive Borel set. We also obtain such a set $A\subseteq T$ simultaneously for continuum many relations $(R_\alpha )_{\alpha <2^\omega }.$ Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.
LA - eng
KW - nonmeasurable set; Bernstein set; Polish ideal space; nonmeasurable set; Bernstein set; Polish ideal space
UR - http://eudml.org/doc/38017
ER -