We study a nonlinear elliptic problem governed by a general Leray-Lions operator
with variable exponents and diffuse Radon measure data that does not charge the sets of zero
p(.)-capacity. We prove a decomposition theorem for these measures (more precisely, as a sum ′
of a function in L1(Ω) and of a measure in W−1,p (.)(Ω)) and an existence and uniqueness result of entropy solution.

Diffuse measure, biting lemma of Chacon, maximal monotone graph, Radon measure data, weak solution, entropy solution, Leray-Lions operator