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either the subset of sequences with 1 in that position or the subset with 0 in that position would have to have measure 1. The intersection of these -many measure 1 subsets would thus also have to have measure 1, but it would contain exactly one sequence, which would contradict the non-triviality of the measure. Thus, assuming the axiom of choice (as the trichotomy of cardinality between κ and 2^λ), we can infer that is a strong limit cardinal,

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