The space (𝑙_{∞}/𝑐₀,𝑤𝑒𝑎𝑘) is not a Radon space

Abstract

Abstract.Talagrand [10] gives an example of a Banach space with weak topology which is not a Radon space, independently of their weight. This result gives an answer to a question formulated by Schwartz [9]. In this paper, following the papers of Drewnowski and Roberts [1] and Talagrand [10], we prove that the classical space (I^/Cq , weak) is not a Radon space.Introduction. A Hausdorff topological space E is said to be a Radon space if every finite Borel measure is a Radon measure; i.e.,