On strong lifting compactness, with applications to topological vector spaces

Abstract

The notion of strong lifting compactness is introduced for completely regular Hausdorff spaces, and its structural properties, as well as its relationship to the strong lifting, to measure compactness, and to lifting compactness, are discussed. For metrizable locally convex spaces under their weak topology, strong lifting compactness is characterized by a list of conditions which are either measure theoretical or topological in their nature, and from which it can be seen that strong lifting compactness is the strong counterpart of measure compactness in that case.

On products of almost strong liftings

“…By the claim W(co) c PiC2C(co,9)) n E, ^( 0 ) c p 2 (<%(co,9)) n rjo,,. This implies p 1 (^'(a),9)) n E = ,0)) 0^ = ^( 0 N. D. Macheras and W. Strauss [14] ty (,u…”