Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator
Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator
Using the variational properties of epi-convergence together with suitable results on the measurability of multifunctions and integrands, we prove a strong law of large numbers for sequences of integrands from which we deduce a general theorem of almost sure convergence (strong consistency) for the maximum likelihood estimator.