It is proved that in a sequential design of a regression problem the variance of the 1.s. estimate for the response surface in the $n$th sequential point tends to zero with $n \rightarrow \infty$. This allows the proof of the convergence of certain procedures for computing $D_s$-optimum designs.
"A Convergence Theorem in the Theory of $D$-Optimum Experimental Designs." Ann. Statist. 2 (1) 216 - 218, January, 1974. https://doi.org/10.1214/aos/1176342628