Modulus of Continuity
- Natural & Formal Sciences -
Mathematics & Logic Dictionary
Definition
A function ω:[0,∞)→[0,∞) with ω(0)=0 and typically nondecreasing such that |f(x)−f(y)| ≤ ω(|x−y|) for all x,y; it quantifies how function variation is controlled by input increments.
Modulus of Continuity
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
A function ω: [0,∞) → [0,∞) that assigns to each scale δ the supremum of |f(x)-f(y)| over all pairs with distance at most δ; it quantifies the maximal oscillation of f at that scale.