On an unbiased estimate with the minimal variance in the class of linear estimates

The paper considers a stochastic process $\xi(t)$ on $[a,b]$ with an unknown mean $m$ and a known correlation function $r(s,t)$. An unbiased estimate for $m$ with the minimal variance in the class of linear estimates is to be found. Using (3), the sequence (5) which converges in mean to the desired estimate is constructed.