A measure extension theorem in l-groups

Alzbeta Michalíková.

In the paper [2] there was proved that if H is a σ-continuous, orthomodular lattice, A is its orthocomplemented sublattice, µ : A → (0,1). is a probability measure that is subadditive and S(A) is the σ-complete orthocomplemented sublattice of H generated by A, then there exist exactly one subadditive probability measure µ : S(A) → (0,1). that is an extension of µ. In the paper we prove the theorem for l-group valued measures that are subadditive. Similar problems were studied for example in [1] and [4].

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