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Left Cauchy Integral Bases in Linear Topological Spaces

Published online by Cambridge University Press:  20 November 2018

James A. Dyer
James A. Dyer*
Affiliation:
Iowa State University, Ames, Iowa
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The purpose of this paper is to consider a representation for the elements of a linear topological space in the form of a σ-integral over a linearly ordered subset of V; this ordered subset is what will be called an L basis. The formal definition of an L basis is essentially an abstraction from ideas used, often tacitly, in proofs of many of the theorems concerning integral representations for continuous linear functionals on function spaces.

The L basis constructed in this paper differs in several basic ways from the integral basis considered by Edwards in [5]. Since the integrals used here are of Hellinger type rather than Radon type one has in the approximating sums for the integral an immediate and natural analogue to the partial sum operators of summation basis theory.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 431 - 439
Copyright
Copyright © Canadian Mathematical Society 1970

References

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