Theory of a Class of Locally Convex Vector Lattices Which Include the Lebesgue Spaces

AUTOR(ES)

Bogdanowicz, Witold M.

RESUMO

In this paper is presented the theory of a class of locally convex lattices (L-lattices) of real functions which generalize the classical Lebesgue spaces. The monotone and dominated convergence theorems for convergence almost everywhere and sequential and order completeness of such lattices are established. These results are obtained through characterization of linear lattices of functions closed under pointwise or dominated convergence everywhere and closed under Stone's operation f → f[unk]1. Such lattices are characterized in terms of measurability with respect to sigma or delta rings.

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