3 citations · 3 across the 3 of their papers we have counts for
5 papers
On random compact sets, equidecomposition, and domains of expansion in R^3
Tomasz Cieśla, Łukasz Grabowski
We study random compact subsets of R^3 which can be described as "random Menger sponges". We use those random sets to construct a pair of compact sets A and B in R^3 which are of t…
On lifting invariant probability measures
Tomasz Cieśla
In this note we study when an invariant probability measure lifts to an invariant measure. Consider a standard Borel space , a Borel probability measure on , a Borel map…
Measurable Hall's theorem for actions of abelian groups
Tomasz Cieśla, Marcin Sabok
We prove a measurable version of the Hall marriage theorem for actions of finitely generated abelian groups. In particular, it implies that for free measure-preserving actions of s…
Completeness of the homeomorphism relation of locally connected continua
Tomasz Cieśla
In this paper we prove that the homeomorphism relation of locally connected continua is a complete orbit equivalence relation. This answers a question posed by Chang and Gao.
A filter on a collection of finite sets and Eberlein compacta
Tomasz Cieśla
We introduce a -ideal on and a filter on the collection of graphs of strictly decreasing partial functions on taking values in . We use them to prove…