In mathematics, a sequence of functions
from a set S to a metric space M is said to be uniformly Cauchy if:
- For all
, there exists
such that for all
:
whenever
.
Another way of saying this is that
as
, where the uniform distance
between two functions is defined by
![{\displaystyle d_{u}(f,g):=\sup _{x\in S}d(f(x),g(x)).}](//wikimedia.org/api/rest_v1/media/math/render/svg/34c7d7181b69fd5d467ddb6ce71a6bf84cad6e92)