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Extra resources for Vector Space Measures and Applications II: Proceedings, Dublin 1977

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Since P is countable, f[XkX O] is separable from which it follows that f is almost separably-valued. 7. M. Sion has proved that if X I is a metric f : X + X] is a multifunction, (i) f is almost immediately provided with a countable (i),(ii),(iii) if and only if separably-valued for every closed F c X I , f I[F] From this result we may ditions then f is partitionahle space and single-valued (ii) f is almost (iii) [] derive that if E is a vector system of seminorms are n e c e s s a r y e H . space P, then the above con- and sufficient for a multifunc- tion f : X ÷ E to be partitionable.

Van N o s t r a n d (1970). Weron, A. ) W o l d - C r a m ~ r c o n c o r d a n c e theorems for 165-183. i n t e r p o l a t i o n of q - v a r i a t e s t a t i o n a r y p r o c e s s e s over locally compact abelian groups, (1976), J. , 6 123-137. D ~ p a r t e m e n t de M a t h ~ m a t i q u e s Ecole P o l y t e c h n i q u e F ~ d ~ r a l e de L a u s a n n e 61Av. de Cour 1007 L A U S A N N E SWITZERLAND. SOME RESULTS WITH RELATION Jens Peter TO THE Reus CONTROL MEASURE PROBLEM Christensen Department of Mathematics, University of Copenhagen, DK-2100 Copenhagen, Denmark.

3. ll~llo,p,z for every N in ~. 4. With f, ¢, and A as above we have n <> : limM[mM=oAn(X) • Proof. 30] we get (i/n:)~n¢(x) Letting ~n TM (i/n~)~nf(0) = [:=O(i/n:)anCm+n(X) . 1 we get co < > = ~=O<~nx,a n Cm+n(X)> n =: An(X) • It is enough now to sum over n. Proposition. 2. )¢>> . 55 Proof. I]. Since the norm of < < . , f ( d , . ) i s l ] F ( d , . 1 can be improved: Corollary. )¢l le, ' (1/~),~ <--- I I+l I e, ,(1/p),=ol I~-I le,p,1/cq 4. E v o l u t i o n e q u a t i o n s goyerne d by ~ ( .

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