A pointwise convergence theorem for sequences of continuous functions.

Author:
K. Schrader

Journal:
Trans. Amer. Math. Soc. **159** (1971), 155-163

MSC:
Primary 40.20

MathSciNet review:
0280902

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Abstract: Let be a sequence of continuous real valued functions defined on an interval and a fixed nonnegative integer such that if for more than distinct values of then for . It follows that there is a subsequence of such that for each the subsequence is eventually monotone. Thus exists for all , where is an extended real valued function. If is bounded for each then exists as a finite limit for all . For this reduces to picking a monotone subsequence from a sequence of continuous functions whose graphs are pairwise disjoint.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0280902-6

Keywords:
Sequences of functions,
pointwise convergence,
boundary value problems,
uniqueness of solutions

Article copyright:
© Copyright 1971
American Mathematical Society