Measurable real-valued function

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Let (X, S) be a measurable space and En measurable sets, not necessarily disjoint, whose union is X. Suppose that for each n, fn is a measurable real-valued function on En. Suppose that for any x ∈ Em ∩ En for any m and n, fm (x ) = fn (x ). Let f (x ) := fn (x ) for any x ∈ En for any n. Show that f is measurable.

Reference no: EM13966756

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