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 compact set compact spaces compact subset completes the proof condition continuous functions continuous linear map converges convex Hausdorff space COROLLARY countable union cylindrical measure defined definition denote disjoint E₁ equivalent finite Borel measure finite measure finite Radon measure follows function f Gauss measure Hausdorff space Hausdorff topological space hence Hilbert space identity map inner regular integrable isonomy class K₁ K₂ Lemma Let f linear random function locally convex Hausdorff Lusin Lusin measurable m-measurable Meas measure µ norm open sets polish space projective limit Prop properties PROPOSITION prove quasi-compact Radon measure Radon space random variable resp satisfying scalarly concentrated sequence strongly Lindelöf surjective Suslin space Suslin subspace Theorem topological space topology unit ball universally measurable v(dy µ(dx