equicontinuous family of functions

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equicontinuous family of functions [¦ē·kwē·kən′tiŋ·yə·wəs ′fam·lē əv ′fəŋk·shənz]

(mathematics)

A family of functions with the property that given any ε > 0 there is a δ > 0 such that whenever |x-y| < δ, |ƒ(x) - ƒ(y)| < ε for every function ƒ(x) in the family. Also known as uniformly equicontinuous family of functions.

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