The universal right K-property for some interpolation spaces
Let ⟨X,Y⟩ be a duality pair of M-spaces X,Y of measurable functions from Ω ⊂ ℝ ⁿ into . The paper deals with Y-weak cluster points ϕ̅ of the sequence in X, where is measurable for j ∈ ℕ and is a Carathéodory function. We obtain general sufficient conditions, under which, for some negligible set , the integral exists for and on , where is a measurable-dependent family of Radon probability measures on .
Sufficient conditions are given in order that, for a bounded closed convex subset of a locally convex space , the set of continuous functions from the compact space into , is the uniformly closed convex hull in of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into .