Lower Bound for the Lebesgue Function of an Interpolation Process with Algebraic Polynomials on Equidistant Nodes of a Simplex

For an interpolation process with algebraic polynomials of degree $n$ on equidistant nodes of an $m$-simplex for $m\ge 2$, we obtain a pointwise lower bound for the Lebesgue function similar to the well-known estimate for interpolation on a closed interval.