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Uniformly Cauchy

The series sum_(j=1)^(infty)f_j(z) is said to be uniformly Cauchy on compact sets if, for each compact K subset= U and each epsilon>0, there exists an N>0 such that for all M>=L>N,

|sum_(j=L)^Mf_j(z)|<epsilon

holds (Krantz 1999, p. 104).

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References

Krantz, S. G. "The Cauchy Condition for a Series." §8.1.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 104, 1999.

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Uniformly Cauchy

Cite this as:

Weisstein, Eric W. "Uniformly Cauchy." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UniformlyCauchy.html

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