Maximum principle for optimal control problems with delays in the non convex case

We establish a stochastic maximum principle for controlled stochastic differential equations with delay and control-dependent noise, without convexity assumptions on the control space. The cost functional depends on both present and delayed states, modeled via general finite measures. For measures with square-integrable densities, we employ infinite-dimensional reformulation and BSDE techniques; for general measures, we apply anticipated BSDEs and weak convergence methods. We further analyze the case of delay measures with $L^p$-densities ($p \in (1,2)$), deriving a generalized mild backward equation beyond Hilbertian settings.