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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Insertion, approximation, and extension of real-valued functions


Authors: Robert L. Blair and Mary Anne Swardson
Journal: Proc. Amer. Math. Soc. 93 (1985), 169-175
MSC: Primary 54C30; Secondary 46E99, 54C05, 54C08, 54C20
DOI: https://doi.org/10.1090/S0002-9939-1985-0766550-5
MathSciNet review: 766550
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Abstract: For a uniformly closed vector lattice $ V$ of real-valued functions on a set $ X$, necessary and sufficient conditions are obtained for insertion (or "strict insertion") of some member of $ V$ between two arbitrary real-valued functions on $ X$. These conditions quickly yield known insertion, approximation, and extension theorems for real-valued functions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766550-5
Keywords: Lebesgue sets, vector lattices of functions, rings of functions, uniform convergence, approximation, extension, insertion, strict insertion, zero-sets
Article copyright: © Copyright 1985 American Mathematical Society