Mackey Continuity of Characteristic Functionals
-
S. Kwapień
Abstract
Problems of the Mackey-continuity of characteristic functionals and the localization of linear kernels of Radon probability measures in locally convex spaces are investigated. First the class of spaces is described, for which the continuity takes place. Then it is shown that in a non-complete sigmacompact inner product space, as well as in a non-complete sigma-compact metizable nuclear space, there may exist a Radon probability measure having a non-continuous characteristic functional in the Mackey topology and a linear kernel not contained in the initial space. Similar problems for moment forms and higher order kernels are also touched upon. Finally, a new proof of the result due to Chr. Borell is given, which asserts that any Gaussian Radon measure on an arbitrary Hausdorff locally convex space has the Mackey-continuous characteristic functional.
© Heldermann Verlag
Articles in the same Issue
- Application of Singular Integral Equations in the Boundary Value Problems of Electroelasticity
- Existence and Properties of ℎ-Sets
- On the Theory of Functional-Differential Inclusion of Neutral Type
- Cesàro Means of Trigonometric Fourier Series
- Estimates of a Stabilization Rate as 𝑡 → ∞ Solutions of a Nonlinear Integro-Differential Equation
- On Kan Fibrations for Maltsev Algebras
- On the Uniqueness Property for Products of Symmetric Invariant Probability Measures
- Mackey Continuity of Characteristic Functionals
- Linear Dynamical Systems: An Axiomatic Approach
- The Bochner Mean Square Deviation and Law of Large Numbers for Squares of Random Elements in Banach Lattices
- A Strong Solution of an Evolution Problem with Integral Conditions
- On Some Properties of 𝑟-Maximal Sets and 𝑄1–𝑁-Reducibility
- On the Dimension of Some Spaces of Generalized Ternary Theta-Series
- Solution of a Linear Integral Equation of Third Kind
- A Semimartingale Bellman Equation and the Variance-Optimal Martingale Measure. Correction
Articles in the same Issue
- Application of Singular Integral Equations in the Boundary Value Problems of Electroelasticity
- Existence and Properties of ℎ-Sets
- On the Theory of Functional-Differential Inclusion of Neutral Type
- Cesàro Means of Trigonometric Fourier Series
- Estimates of a Stabilization Rate as 𝑡 → ∞ Solutions of a Nonlinear Integro-Differential Equation
- On Kan Fibrations for Maltsev Algebras
- On the Uniqueness Property for Products of Symmetric Invariant Probability Measures
- Mackey Continuity of Characteristic Functionals
- Linear Dynamical Systems: An Axiomatic Approach
- The Bochner Mean Square Deviation and Law of Large Numbers for Squares of Random Elements in Banach Lattices
- A Strong Solution of an Evolution Problem with Integral Conditions
- On Some Properties of 𝑟-Maximal Sets and 𝑄1–𝑁-Reducibility
- On the Dimension of Some Spaces of Generalized Ternary Theta-Series
- Solution of a Linear Integral Equation of Third Kind
- A Semimartingale Bellman Equation and the Variance-Optimal Martingale Measure. Correction
