**S. Kwapien, V. Tarieladze**

##
Mackey Continuity of Characteristic Functionals

**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 sigma-compact inner product space, as well as in a non-complete
sigma-compact metrizable 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.