Uniformly exhaustive submeasures and nearly additive set functions

Every uniformly exhaustive submeasure is equivalent to a measure. From this, we deduce that every vector measure with compact range in an F F -space has a control measure. We also show that c 0 c₀ (or any L ∞ {L_ } -space) is a K K -space, i. e. cannot be realized as the quotient of a nonlocally convex F F -space by a one-dimensional subspace.