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Let $Q=(0,T)\times\Omega$, where $\Omega$ is a bounded open subset of$\mathbb{R}^d$. We consider the parabolic $p$-capacity on $Q$ naturallyassociated with the usual $p$-Laplacian. Droniou, Porretta and Prignet haveshown that if a bounded Radon measure $\mu$ on $Q$ is diffuse, i.e. charges noset of zero $p$-capacity, $p>1$, then it is of the form$\mu=f+\mbox{div}(G)+g_t$ for some $f\in L^1(Q)$, $G\in (L^{p'}(Q))^d$ and$g\in L^p(0,T;W^{1,p}_0(\Omega)\cap L^2(\Omega))$. We show the converse of thisresult: if $p>1$, then each bounded Radon measure $\mu$ on $Q$ admitting such adecomposition is diffuse.

On the structure of diffuse measures for parabolic capacities