# Aleksander Cieślak: On nonmeasurable subsets of $\mathbb{R}$ and $\mathbb{R}^2$

Tuesday, October 27, 2015, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Aleksander Cieślak (Wrocław University of Technology)

Title: On nonmeasurable subsets of $\mathbb{R}$ and $\mathbb{R}^2$

Abstract:

I would like to present some results connected with the existence of a subset $X$ of the square $[0,1]^2$ with the property that for any line $L$ outside $[0,1]^2$ the projection $\pi_L[X]$ is completely nonmeasurable in some interval with respect to selected $sigma$-ideal with Borel base on the line $L$.

Moreover, I will discuss the existence of large midpoint-free subsets of arbitrary subset of the real line.