In this research work, we introduce a new concept of double measure ergodic processes to identify the space of double measure pseudo almost periodic (or pap) processes in the pth mean sense. We display some findings regarding the completeness as well as the composition theorems and the invariance of the space consisting in double measure pap processes. Motivated by the above-mentioned results, the Banach fixed point theorem and the stochastic analysis techniques, we prove the existence, uniqueness and the global exponential stability of doubly measure pseudo almost periodic mild solution for a class of stochastic Nicholson's blowflies model with mixed delays in a separable real Hilbert space. The concluding part of the work is crowned with an example to confirm the reliability and feasibility of our findings.