In this talk, we consider porous medium type equations with measurable coefficients when the right-hand side is a nonnegative Radon measure with finite total mass. We discuss integrability results for the spatial gradient of a solution in the setting of the Marcinkiewicz space, under a suitable density condition of the right-hand side measure. We also introduce a notion of solution which guarantees the regularity results. This is joint work with Sukjung Hwang.