examples of sets of weight functions satisfying the above conditions are the positive polynomials and positive simple functions in [@rud Definition 1.16]. In general, the positive linear combinations of a Chevyshev system (see [@KN Chapter II]) conform a set as $\Phi$. Examples of Chevyshev systems can be found in [@nik] (also in [@FMM]).

Given $\rho \in \Phi$ we set $${\bf v}_{\rho}=\left(\int \widetilde{P}_n(x)\rho(x) \mbox{d} \mu(x), \ldots, \int x^{n-2} \widetilde{P}_n(x)\rho(x) \mbox{d} \mu(x),\right.$$ $$\left.\int P_{n}(x)\rho(x) \mbox{d} \mu(x), \ldots,\int x^{n-1} P_{n}(x)\rho(x) \mbox{d} \mu(x)\right)\in \mathbb{R}^{2n-1}.$$ Let us focus on $\mathcal{K}=\left\{{\bf v}_{\rho}:\rho \in \Phi\right\}$. Proving Lemma \[interwendroff\] reduces to showing that $\mathcal{K}$ contains the origin. From condition $(i)$ we have that the origin belongs to $\mathcal{K}$’s closure, $\overline{\mathcal{K}}$. Since $\mathcal{K}$ is open we need to prove the origin is an interior point. We proceed by contradiction. Suppose that the origin belongs to the boundary of $\mathcal{K}$. This is ${\bf O}\in \partial \mathcal{K}= \overline{K}\setminus \mathcal{K}$. There exists a hyper-plane $\mathcal{A}$ that touches tangentially $\partial \mathcal{K}$ at ${\bf O}$. On the other hand we have that condition (ii) implies that $\mathcal{K}$ is convex, then there exists a vector $\displaystyle {\bf a}=\left(a_{0,n-1}, \ldots, a_{n-2,n-1},a_{0,n},\ldots,a_{n-1,n}\right)$ which is orthogonal with respect to $\mathcal{A}$ in the sense of the standard inner vector 