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Decomposition of $ℓ$ -group-valued measures

Giuseppina Barbieri; Antonietta Valente; Hans Weber — 2012

Czechoslovak Mathematical Journal

We deal with decomposition theorems for modular measures $μ : L \to G$ defined on a D-lattice with values in a Dedekind complete $ℓ$ -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete $ℓ$ -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for $ℓ$ -group-valued...

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Decomposition of ℓ -group-valued measures

Decomposition of $ℓ$ -group-valued measures