Absolute continuity of functionals of “supremum” type for Gaussian processes

In the paper one gives certain sufficient or necessary and sufficient conditions for the absolute continuity of the functional where X_t is a continuous Gaussian process on a compact parameter space T.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 119, pp. 154–166, 1982.