We study Beck-like coloring of measurable functions on a measure space Ω taking values in a measurable semigroup Δ . To any measure space Ω and any measurable semigroup Δ , we assign a graph (called a zero-divisor graph) whose vertices are labeled by the classes of measurable functions defined on Ω and having values in Δ , with two vertices f and g adjacent if f g = 0 a. e. . We show that, if Ω is atomic, then not only the Beck’ s conjecture holds but also the domination number coincides to the clique number and chromatic number as well. We also determine some other graph properties of such a graph.