Continuous ergodic measures on 𝑅^{∞} have disjoint powers

Kanter, Marek

doi:10.1090/S0002-9939-1977-0443067-4

Continuous ergodic measures on $R^{\infty }$ have disjoint powers
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Proc. Amer. Math. Soc. 65 (1977), 332-337 Request permission

Abstract:

If $\mu$ is an ergodic probability measure on an infinite dimensional linear measure space and if there exists an infinite sequence of measurable linear functional on this space such that all nontrivial linear combinations have continuous distribution under $\mu$, then the convolution powers of $\mu$ all live on disjoint sets.

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