Abstract
In this paper we shall prove that the extension Î of a generalized (or full) Daniell-integral I over a non distributive lattice Ê with values in a weakly б-distributive 1-group G has all the fundamental limiting properties of the Lebesgue integral, i.e. the properties stated i n the monotone convergence theorem, Fatou's-lemma and Lebesgue's dominated convergence theorem.
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