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LAURENT P. Approximation ROCKAFELLAR, et Optimisation, [PARIS) 1972. T. Convex Analysis, Princeton SCHWARTZ Hermann University Press [197Q] L. [1] Notes manuscrites [2] Probabilit@s non publi@es cyllndriques faculty of Science, et applications University radonifiantes, Journal of the of ToKyo, Vol. 18, n ° 2, pp. 139-186~ 1970. Dept. R. P. 45, 63170 Aubiere, ~NCE. ABSOLUTE CONTINUITY FOR A CLASS OF PROBABILITY MEASURES Charles R. Baker* University of North Carolina Chapel Hill, North Carolina Introduction Let 8 be a real separable Banach space with Borel o-field B[B], and let ~I and ~2 be two probability measures on B[8].
Ro Baker, On equivalence of probability measures, Ann. Probability, i, 690698 (1973). R. Baker, Joint measures and cross-covariance (1973). , 186, 273-289 operators, Trans. American Math. 50 3. 4. G. Douglas, On majorization, factorization, and range inclusion of operators in Hilbert space, Proc. American Math. , 17, 413-415 (1966). J. Feldman, Equivalence and perpendicularity of Gaussian processes, Pacific J. , 8, 699-708 (1958). 5. R. Fortet, Espaces ~ noyau reproduisant et lois de probabilit6s des fonctions al6atoires, Ann.
I, pour q{Y,X 1) de ~. - Solent F61[P) = ~1[~1 ). comma ci-dessus 8 et soit 8 c £o(X,Y)). i, (:1{~1) Si B~ e s t p * [ B ~) X > 0 , y c XB} homog6ne. ~ puisque + [1 - ~ I ( B ~ } } ~*(~) ~[X,Y)-compect (I~1) de ~ precedent. Solt ~ la jauge de B : {X, entre {X, X 1, Y, #, pl ) comma dens le th~or~me 4, et soit B c Y. = ~,(a El) ~ ( o ) V con- de X. Alors ]. est positivement c~*(~) ~ soit Supposons p scaleirement la polaire de B dens X, B I la polaire de B dens X 1 ; on e alors v [3 v ~(B ) = "P1[8 et et ( c a r e 1 e s t de M o r e e u ) .