Additive functions modulo a countable subgroup of ℝ

Nikos Frantzikinakis

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Functions Equivalent to Borel Measurable Ones

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Let X and Y be two Polish spaces. Functions f,g: X → Y are called equivalent if there exists a bijection φ from X onto itself such that g∘φ = f. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.

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We consider some descriptive properties of supports of shift invariant measures on $ℂ^{ℤ}$ under the assumption that the closed linear span (in $L^{2}$ ) of the co-ordinate functions on $ℂ^{ℤ}$ is all of $L^{2}$ .

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