Riesz potential estimates for parabolic equations with measurable nonlinearities

We study a nonlinear parabolic equation with measurable nonlinearity and measure data: ut-div a(Du,u, x, t) = μ in ωT . We obtain an optimal point-wise estimate for the gradient of a solution in terms of a certain Riesz potential of the right-hand measure in a very general setting that the nonlinearity is not only allowed to be measurable in one of spatial variables, but also depends on the variable of the possibly unbounded solution itself.