equicontinuous family of functions

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,="">x) - ƒ(y)| < ε="" for="" every="" function="">x) in the family. Also known as uniformly equicontinuous family of functions.