### A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations

The exit distribution for open sets of a path-continuous, strong Markov process in ${\mathbf{R}}^{n}$ is characterized as a weak star limit of successive spherical sweepings of measures, starting with the unit point mass. Then this is used to prove that two path-continuous strong Markov processes with identical exit distributions from balls when starting form the center, have identical exit distributions from all opens sets, provided they both exit a.s. from bounded sets. This implies that the only path-continuous,...