Two Examples Concerning a Theorem of Burgess and Mauldin

Abstract

We show that for the transition kernels $(\mu_y)$ of a certain random walk in $\mathbb{R}^2$ and the Radon Transform in $\mathbb{R}^3$ there is no subset $K$ of positive Lebesgue-measure such that $(\mu_y)_{y\in K}$ is completely orthogonal.