User guide to transverse measure theory

A cross-section of a dynamical system $(G,X)$ is a subset $Y$ of $X$ such that $GY=X$ . Transverse measure theory concerns itself with connections between measures on $Y$ and measures on $X$ . We will learn how one can integrate special measures on $Y$ to $G$ -invariant measures on $X$ and disintegrate $G$ -invariant measures on $X$ to measures on $Y$ . We will further see how one can apply the theory to examples from the field of aperiodic order.