In this paper we characterise the Lp stability of the following perturbed linear Volterra integrodifferential convolution equation, x′(t)=∫[0,t]ν(ds)x(t−s)+f(t),t≥0,where ν is a finite signed Borel measure. Additionally we provide a framework which points to necessary and sufficient conditions on the forcing function that ensures the solution lies in a particular function space. We highlight how such a result is of interest when studying perturbed Stochastic Functional Differential Equations (SFDEs).