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In this paper we suggest a measure free construction of      L 1 {L^1}      -spaces using Boolean algebras and strict topologies and initiate a duality theory of      ( L ∞  , L 1 ) ({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      σ  \sigma      -additivity and uniform integrability.

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