We prove an algebraic and a topological decomposition theorem for complete D-lattices (i.e., lattice-ordered effect algebras). As a consequence, we obtain a HammerSobczyk type decomposition theorem for modular measures on D-lattices.

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Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations and ⊕ of L are uniquely determined by their system of neighborhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0, +∞]-valued functions on L.

We prove a Carathéodory type extension theorem for