Convergence in measure refers to a sequence of measurable functions that approaches a limiting function in the sense that, for any given positive tolerance, the measure of the set where the functions deviate from the limit exceeds that tolerance goes to zero. This concept is closely tied to measure spaces and measurable functions, as it helps establish the behavior of sequences of functions under the framework of measure theory, allowing us to understand how these functions behave almost everywhere and how limits can be formed in this context.
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