Lp-valued random measures and good extensions of a stochastic basis

In this paper, a development of the author's paper [Theory Probab. Appl., 40 (1995), pp. 645-652], we prove the existence of an extension of an L-p-valued random measure theta in the sense of Bichteler and Jacod Theory and Application of Random Fields, Lecture Notes in Control and Inform. Sci. 49, Springer, Berlin, 1983, pp, 1 [8] under a good (with respect to theta) extension of a stochastic basis, Our main result, Theorem 2, wild announced in [V. A, Lebedev, Proc. 22nd European Meeting of Statisticians and 7th Vilnius Conference on Probability Theory and Mathematical Statistics: Abstracts of Communications, TEV, Vilnius, 1998, p. 298].