We study a nonlinear anisotropic elliptic problem with homogeneous Neumann boundary condition governed by a general anisotropic operator with variable exponents and diffuse Radon measure data that is the Radon measure which does not charge the sets of zero p(⋅)-capacity. We firstly prove the existence of renormalized solutions. Secondly, we show an equivalence between renormalized solution and entropy solution. Thirdly, we end by proving an uniqueness result of entropy solution

Neumann boundary; anisotropic Sobolev spaces; renormalized solution; entropy solution; maximal monotone graph; Radon diffuse measure; Marcinkiewicz spaces; p(⋅)-capacity