Geometric Measure Theory
The Lipschitz condition is a criterion for measuring the rate at which a function can change. A function satisfies the Lipschitz condition if there exists a constant $L \geq 0$ such that for any two points $x$ and $y$ in its domain, the inequality $|f(x) - f(y)| \leq L |x - y|$ holds. This concept is crucial as it establishes a bound on how steeply the function can rise or fall, ensuring that small changes in the input lead to controlled changes in the output.
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