Aleksander Cieślak: On nonmeasurable subsets of \(\mathbb{R}\) and \(\mathbb{R}^2\)
21/10/15 21:14
Tuesday, October 27, 2015 17:15
Room: D1-215
Speaker: Aleksander Cieślak
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.
Room: D1-215
Speaker: Aleksander Cieślak
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.