Convergence in measure refers to a type of convergence for a sequence of measurable functions, where the measure of the set of points where the functions deviate from a limiting function exceeds any small positive threshold tends to zero as the sequence progresses. This concept is crucial in understanding how functions behave as they approach a limit, particularly in the context of integrable functions and measurable spaces. It provides a framework for assessing the closeness of these functions in a probabilistic sense, connecting with various tests for convergence.
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