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The goal of this paper is to canonize Borel measurable mappings ∆: Ωω → R, where Ωω is the Milliken space, i.e., the space of all increasing infinite sequences of pairwise disjoint nonempty finite sets of ω .T his main result is a common generalization of a theorem of Taylor and a theorem of Promel and Voigt.

Canonical forms of Borel functions on the Milliken space