Convergent subsequences from sequences of functions
Author:
James L. Thornburg
Journal:
Trans. Amer. Math. Soc. 208 (1975), 171192
MSC:
Primary 40A05; Secondary 26A45, 46A40
MathSciNet review:
0372458
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Abstract 
References 
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Abstract: Let be a sequence of functions, where is a nonempty subset of the dimensional Euclidean space and is an ordered vector space with positive cone . If , sufficient conditions are given that have a subsequence such that for each the sequence is monotone for sufficiently large, depending on . If each is an ordered topological vector space, sufficient conditions are given that has a subsequence such that for every the sequence is either monotone for sufficiently large depending on , or else the sequence is convergent. If for each and a Banach space then a definition of bounded variation is given so that if is uniformly norm bounded and the variation of the functions is uniformly bounded then there is a convergent subsequence of . In the case for each and is such that bounded monotone sequences converge then the given conditions imply the existence of a subsequence of which converges for each .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197503724588
PII:
S 00029947(1975)03724588
Keywords:
Sequences of functions,
convergence of subsequences,
monotonicity of subsequences,
variation,
functions of bounded variation,
ordered topological vector spaces
Article copyright:
© Copyright 1975
American Mathematical Society
