Dini continuity
From Infogalactic: the planetary knowledge core
In mathematical analysis, Dini continuity is a refinement of continuity. Every Dini continuous function is continuous. Every Lipschitz continuous function is Dini continuous.
Definition
Let be a compact subset of a metric space (such as
), and let
be a function from
into itself. The modulus of continuity of
is
The function is called Dini-continuous if
An equivalent condition is that, for any ,
where is the diameter of
.
See also
- Dini test — a condition similar to local Dini continuity implies convergence of a Fourier transform.
References
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