1 citations · 1 across the 6 of their papers we have counts for
6 papers
On some geometrization of compact metric spaces: A solution to the Banach-Ulam conjecture
Grzegorz Tomkowicz
We propose a geometrization of compact metric spaces that is based on ideas of S. Banach and J. Mycielski. Then we prove the following conjecture of S. Banach and S. Ulam from 1935…
Paradoxical decompositions and finitary colouring rules
Robert Samuel Simon, Grzegorz Tomkowicz
We define "paradoxical colouring rule", show its relation to measure theoretic paradoxes, and demonstrate that proper vertex colouring can be a paradoxical colouring rule.
A Measure Theoretic Paradox from a continuous colouring rule
Robert Simon, Grzegorz Tomkowicz
Given a probability space , measure preserving transformations of , and a colour set , a colouring rule is a way to colour the space with…
A Continuous Paradoxical Colouring Rule Using Group Action
Tugkan Batu, Robert Samuel Simon, Grzegorz Tomkowicz
Given a probability space , measure preserving transformations of , and a colour set , a colouring rule is a way to colour the space with…
Paradoxical decompositions and finitary rules
Robert Samuel Simon, Grzegorz Tomkowicz
We colour every point x of a probability space X according to the colours of a finite list x_1, ...., x_k of points such that each of the x_i, as a function of x, is a measure pres…
A Bayesian Game without epsilon equilibria
Robert Samuel Simon, Grzegorz Tomkowicz
We present a three player Bayesian game for which there is no epsilon equilibria in Borel measurable strategies for small enough epsilon, however there are non-measurable equilibri…