Question: A continuous function on a compact domain is uniformly continuous. In economic analysis, uniform continuity typically takes a slightly stronger form. A function f: X

A continuous function on a compact domain is uniformly continuous. In economic analysis, uniform continuity typically takes a slightly stronger form. A function f: X → Y is Lipschitz (continuous) if there is a constant b such that for every x, x0 ∊ X,
p (f(x), f(x0)) ≤ βp(x, x0)
β is called the Lipschitz constant or modulus.

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