Let $ L $ be a lattice ordered effect algebra. We
prove that the lattice uniformities on $ L $ which makes $ \ominus
$ and $ \oplus $ uniformly continuous form a Boolean algebra
isomorphic to the centre of a suitable complete effect algebra
associated to $ L. $ As a consequence, we obtain decomposition
theorems - such as Lebesgue and Hewitt-Yosida decompositions - and
control theorems - such as Bartle-Dunford-Schwartz and Rybakov
theorems - for modular measures on $ L. $