  Let $n$ be an odd positive integer. It was proved by Brass and Schmeisser
that for every quadrature $$\mathcal{Q}=\alpha_1f(x_1)+\dots+\alpha_mf(x_m),$$
(with positive weights) of order at least $n+1$ and for every $n-$convex
function $f,$ the value of $Q$ on $f$ lies between the values of Gauss and
Lobatto quadratures of order $n+1$ calculated for the same function $f$. We
generalize this result in two directions, replacing $Q$ by an integral with
respect to a given measure and allowing the number $n$ to any positive integer
(for even $n$ Radau quadratures replace Gauss and Lobatto ones
