On the theory of large deviations

The similarity of the “large deviation principle, (DV1) and (DV2)” and the “weak convergence of probability measures” was used by the author in the earlier paper [9] to study the rough asymptotic behavior of large deviations by the techniques of the theory of weak convergence. This paper is a continuation of [9]. A simpler proof is given for one of the main results of [9] (“if a sequence of measures is exponentially tight, then it is relatively compact in the sense of large deviations”). The problem of large deviations for semimartingales is considered.