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V. Baumann, J. Pfanzagl (1966)
The closure operator in partial algebras with distributive operations. Applications to set algebra, measure theory and linear spacesMathematische Zeitschrift, 92
N. Bourbaki (1965)
Livre VI. Intégration, Chap. I–IV
P.R. Halmos (1950)
Measure theory
G. Birkhoff (1948)
Lattice theory
In this paper the concept of distributivity introduced earlier [1] is used to show that a homomorphism with respect to two distributive operations which is extended as a homomorphism with respect to operation 1 remains necessarily also a homomorphism with respect to operation 2 on the 1-closure of the original domain of definition. The result is illustrated by applications to continuous extensions of homomorphisms between δ-complete vector lattices, association of families of stochastically independent systems of sets and integration of products of independent functions.
Mathematische Zeitschrift – Springer Journals
Published: Jan 22, 2005
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