| 释义 |
uniformly continuous A function f :I → R, defined on an interval I, is uniformly continuous if, for every ε>0, there exists a single δ > 0 such that, for all x,y ε I satisfying |y − x| < δ, then |f(y) − f(x)| < ε. For continuity only, the value of δ typically depends on x as well as ε. The notion extends readily to metric spaces, and continuous functions on a compact space are uniformly continuous. Absolutely continuous functions are uniformly continuous, but the converse does not hold (see Cantor distribution).
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