抄録
Let \mathscr{M} be the class of barrelled locally convex Hausdorff space E such that Eb' satisfies the property B in the sense of Pietsch. It is shown that if E∈\mathscr{M} and if each continuous cylinder set measure on E' is σ(E', E) -Radon, then E is nuclear. There exists an example of non-nuclear Fréchet space E such that each continuous Gaussian cylinder set measure on is E' is σ(E', E)-Radon. Let q be 2≤ q<∞. Suppose that E∈\mathscr{M} and E is a projective limit of Banach space {Eα} such that the dual Eα' is of cotype q for every α. Suppose also that each continuous Gaussian cylinder set measure on E' is σ(E', E)-Radon. Then E is nuclear.
