Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures

assume Banach space bijective Borel measure Borel o-algebra Borel set Borel subset bounded canonical injection Chap closed subspace compact set compact spaces compact subset completes the proof concentrated cylindrically condition continuous functions continuous linear map convex Hausdorff space COROLLARY countable countable union cylindrical measure defined definition denote E₁ equipped equivalent exists finite Radon measure follows function f Gauss measure hence Hilbert space Hilbert subspace identity map inner regular integrable isonomy class Lemma Let f linear form linear random function locally convex Hausdorff Lusin Lusin measurable map f Meas morphism neighbourhood norm nuclear open sets polish space projective limit Prop PROPOSITION prove Radon measure Radon space radonifying random variable scalarly concentrated sequence surjective Suslin space T₁ Theorem topological space u-measurable unit ball universally measurable weakly compact X₁ μ₁