1. On nonmeasurable images
- Creator:
- Rałowski, Robert and Żeberski, Szymon
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- nonmeasurable set, Bernstein set, and Polish ideal space
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public