An 𝐿¹-space for Boolean algebras and semireflexivity of spaces 𝐿^{∞}(𝑋,Σ,𝜇)

Abstract

Abstract. In this paper we suggest a measure free construction of Ù-spaces using Boolean algebras and strict topologies and initiate a duality theory of (LM,l}) like that of the duality of continuous functions and Baire measures, showing that the Boolean context yields a formal link between uniform tightness, uniform o-additivity and uniform integrability.