Paradoxical Decompositions and Colouring Rules

Authors

Robert Simon, London School of Economics and Political Science

Document Type

Lecture

Publication Date

4-3-2024

Abstract

A colouring rule is a way to colour the points x of a probability space according to the colours of finitely many measure preserving transformations of x. The rule is paradoxical if the rule can be satisfied a.e. by some colourings, but by none whose inverse images are measurable with respect to any finitely additive extension for which the transformations remain measure preserving. Weshowthat there is a paradoxical colouring rule when the rule is continuous and we show that proper colouring can be paradoxical.

Relational Format

presentation

Recommended Citation

Simon, Robert, "Paradoxical Decompositions and Colouring Rules" (2024). Combinatorics Seminar. 9.
https://egrove.olemiss.edu/math_combinatorics/9