Convergence in measure is a concept in measure theory that refers to a sequence of measurable functions converging to a limit function in a way that the measure of the set where they differ significantly shrinks to zero as the sequence progresses. This type of convergence is particularly useful when dealing with integration and properties of functions, allowing for the interchange of limits and integrals under certain conditions. It's closely related to Caccioppoli sets, where the idea of convergence plays a crucial role in understanding the structure and behavior of these sets, as well as in the context of differentiability almost everywhere.
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