%0 Journal Article
%A Bombal Gordón, Fernando
%T On the space Lp(μ,X). (Spanish: Sobre el espacio Lp(μ,X)).
%D 1980
%@ 0034-0596
%U https://hdl.handle.net/20.500.14352/64746
%X Letting X  be a Banach space, (S,μ,Σ)  a space of finite measure, 1<p<∞ , and L p (μ,X)  the space of functions from S  into X  with |f| p   integrable, the author studies the dual pair (L p (μ,X),L q (μ,X ′ )). He gives necessary conditions, which are also sufficient if X  has the Radon-Nikodým property, in order that a subset of L p (μ,X)  be σ(L p (μ,X),L q (μ,X ′ )) -relatively sequentially compact and shows that L p (μ,X)  is σ(L p (μ,X),L q (μ,X ′ ))  sequentially complete for every finite measure μ  if and only if X  is weakly sequentially complete and has the Radon-Nikodým property.
%~