### Homogeneous chaos revisited

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Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves.

In this note, I will summarize and make a couple of small additions to some results which I obtained earlier with David Williams in [1]. Williams and I hope to expand and refine these additions in a future paper based on work that is still in process.

The article presents the life and achievements of Mark Kac, the great Polish and American mathematician, as seen and personally remembered by his former PhD student.

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,...

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