%0 Journal Article
%A Bombal Gordón, Fernando
%T The Radon-Nikodým theorem in bornological spaces. (Spanish: El teorema de Radon-Nikodym en espacios bornológicos).
%D 1981
%@ 0034-0596
%U https://hdl.handle.net/20.500.14352/64748
%X The author presents some Radon-Nikodým theorems—i.e., if (Ω,Σ,μ)  is a finite measurable space and m  is a μ -continuous vector measure then {m(A)/μ(A):A∈Σ}  being compact in some sense implies that m  is an integral. Theorem 6: One has a Radon-Nikodým theorem for Fréchet spaces. Theorem 8: One has a Radon-Nikodým theorem for vector measures of finite variation and for a quasicomplete space E  with the metrizable Pietsch property. (E  is said to have the metrizable Pietsch property if X⊂E N   with ∑p(x n )<∞  for each (x n )∈X  and each continuous seminorm p  implies the existence of a B , B⊂E , absolutely convex, bounded and metrizable, with gauge P B  , and such that ∑P B (y n )≤1  for each (y n )∈X .)    G. Y. H. Chi proved this result [Measure theory (Oberwolfach, 1975), pp. 199–210, Lecture Notes in Math., 541, Springer, Berlin, 1976; with a compactness hypothesis for m(A)/μ(A) , instead of weak compactness.  Unfortunately the proofs are not quite clear or even quite exact. In the reference to the Grothendieck book there is a B  instead of an 8.
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