Abstract
Let H1 (resp., H2) be a real and separable Hilbert space with Borel o-field r1 (resp., r2), and let (H1 x H2, r, x r2) be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on (H1 x H2, rJ x r2), i.e., joint measures, and the projections of such measures on (H1, rl) and (H2, r2). In particular, the class of all joint Gaussian measures having two specified Gaussian measures as projections is characterized, and conditions are ob- tained for two joint Gaussian measures to be mutually absolutely continuous. The cross-covariance operator of a joint measure plays a major role in these results and these operators are characterized. (*) IH ~~~~~~~~~llx 11 2 djLi(x) < oo
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