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An $ L\sp{1}$-space for Boolean algebras and semireflexivity of spaces $ L\sp{\infty }(X,\Sigma ,\mu )$


Author: Dennis Sentilles
Journal: Trans. Amer. Math. Soc. 226 (1977), 1-37
MSC: Primary 46E30
DOI: https://doi.org/10.1090/S0002-9947-1977-0430769-3
MathSciNet review: 0430769
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Abstract: In this paper we suggest a measure free construction of $ {L^1}$-spaces using Boolean algebras and strict topologies and initiate a duality theory of $ ({L^\infty },{L^1})$ like that of the duality of continuous functions and Baire measures, showing that the Boolean context yields a formal link between uniform tightness, uniform $ \sigma $-additivity and uniform integrability.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0430769-3
Article copyright: © Copyright 1977 American Mathematical Society

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