In this study, we establish the existence of a renormalized solution for nonlinear parabolic problems characterized by measure data within the context of Musielak spaces. Our analysis involves the Leray-Lions operator, which maps from \(W^{1,x}_0 L_{\varphi }(Q)\) to its dual space, and includes two lower order terms. In this framework, \(\varphi\) represents a Musielak function. It is important to note that the two lower-order terms, \(G(x,t,\varpi ,\nabla \varpi )\) and \(h(x,t,\nabla \varpi )\) , satisfy only a growth condition. One for G is limited by \(\varphi\) , while the other for h is bounded by \(\overline{\gamma }_x^{-1} \gamma _x(\nabla \varpi )\) , where \(\gamma\) also denotes a Musielak function ( \(\gamma\) grows essentially less rapidly than \(\varphi\) at 0).
