Geodesic
Radon Measures on Banach Spaces with their Weak Topologies
Serdica Mathematical Journal, Tome 21 (1995) no. 4, pp. 283-334.

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The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.
Keywords: Banach Space, Weak Topology, Borel Measure, Radon Measure 
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Jayne, J.; Rogers, C. Radon Measures on Banach Spaces with their Weak Topologies. Serdica Mathematical Journal, Tome 21 (1995) no. 4, pp. 283-334. http://geodesic.mathdoc.fr/item/SMJ2_1995_21_4_a1/