**Nguyen Duy Tien, V. Tarieladze**

## Probability Measures with Big Kernels

**abstract:**

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.