Definition for "Lipschitz Continuity" in the Quantum Dictionary

Natural & Formal Sciences Dictionary

A function f between metric spaces is Lipschitz continuous if there exists a constant L≥0 such that for all x,y the distance between f(x) and f(y) is at most L times the distance between x and y.

- Mathematics & Logic -

Pure Mathematics Dictionary

There exists a constant L≥0 such that for all x,y in the domain, d(f(x),f(y)) ≤ L·d(x,y). The smallest such L is called a Lipschitz constant. This provides a global linear bound on increments.