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Proceedings of the American Mathematical Society

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

 

 

Inverse systems of abstract Lebesgue spaces


Author: Bruce Christianson
Journal: Proc. Amer. Math. Soc. 110 (1990), 855-857
MSC: Primary 46M10; Secondary 46B25
DOI: https://doi.org/10.1090/S0002-9939-1990-1030734-3
MathSciNet review: 1030734
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Abstract: We show that inverse limits exist in the category of $ {L^1}$ spaces and positive linear contractions between them. This result generalizes the wellknown classical results for inverse systems of Choquet Simplexes and of $ L$-balls, but our proof is simple and more purely geometrical. The result finds physical application in the study of random fields.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1030734-3
Article copyright: © Copyright 1990 American Mathematical Society