If z is a function from the real line R′ to a real Hilbert space X then the covariance function ϱ of z is defined by ϱ(t, s) ≡ (z(t), z(s)). It is proved that the function (z(·), y) is of bounded ...

Cramer's theorem, that a normal distribution function $(\operatorname{df})$ has only normal components, is extended to a case where the components are allowed to be from a subclass $(B_1)$ of the ...