Kawabe, Jun Sequential compactness for the weak topology of vector measures in certain nuclear spaces. (English) Zbl 1023.28008 Georgian Math. J. 8, No. 2, 283-295 (2001). Let \(S\) be a completely regular Hausdorff space, \(X\) a semi-Montel space and \(M_t(S,X)\) the space of all \(X\)-valued Radon measures on \(S\) endowed with the weakest topology which makes \(\mu\to \int f d\mu\) continuous for every continuous bounded real-valued function \(f\) on \(S\). The author proves that a subset \(V\) of \(M_t(S,X)\) is relatively compact if \(\{x^*\mu: \mu\in V\}\) is relatively compact in \(M_t(S,\mathbb{R})\) for every \(x^*\in X^*\). Moreover, it is given a criterion for metrizability of \(V\). Reviewer: Hans Weber (Udine) Cited in 1 Review MSC: 28B05 Vector-valued set functions, measures and integrals 46G10 Vector-valued measures and integration 28C15 Set functions and measures on topological spaces (regularity of measures, etc.) Keywords:vector measure; weak compactness; Hausdorff space; semi-Montel space × Cite Format Result Cite Review PDF Full Text: EuDML