Ergodic Theory
Uniform convergence is a type of convergence for sequences of functions where the rate of convergence is consistent across the entire domain. This means that given a sequence of functions, they converge to a limiting function uniformly if for any small positive number, there exists a point in the sequence such that the difference between the functions and the limit can be made uniformly small for all points in the domain. Understanding uniform convergence is crucial when dealing with continuity and integration properties of function sequences, especially in the context of equicontinuity and systems that are considered distal.
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