Let [itex]Z:= A^T[/itex], where [itex]T[/itex] is a countable set and [itex]A[/itex] is a finite set. Under the product topology, [itex]Z[/itex] is a compact metrizable space. (As a special case, notice that [itex]Z[/itex] could be the Cantor set).(adsbygoogle = window.adsbygoogle || []).push({});

Given a closed set [itex]X \subseteq Z[/itex], I'm interested in answering the question, "Does there exist some partition [itex]\mathcal P[/itex] of [itex]T[/itex] such that [itex]X = \{f \in Z: \enspace f \text{ is } \mathcal P\text{-measurable}\}[/itex]?"

Is anybody here aware of any alternative formulations of the above question? For example, is there a topological characterization?

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# Equivalent conditions for a measurability restriction?

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