Nguyen Duy Tien, V. Tarieladze

Probability Measures with Big Kernels

It is shown that in an infinite-dimensional dually separated second category topological vector space $X$ there does not exist a probability measure $\mu$ for which the kernel coincides with $X$. Moreover, we show that in ``good'' cases the kernel has the full measure if and only if it is finite-dimensional. Also, the problem posed by S. Chevet in 1981 is solved by proving that the annihilator of the kernel of a measure $\mu$ coincides with the annililator of $\mu$ if and only if the topology of $\mu$-convergence in the dual space is essentially dually separated.