In this paper the concept of distributivity introduced earlier  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.
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Pfanzagl, J. Homomorphisms for distributive operations in partial algebras. Applications to linear operators and measure theory. Math Z 99, 270–278 (1967). https://doi.org/10.1007/BF01112456
- Linear Operator
- Vector Lattice
- Measure Theory
- Continuous Extension
- Independent Function