On weighted Lebesgue function type sums

Let I   be a finite or infinite interval and dμdμ a measure on I  . Assume that the weight function w(x)>0w(x)>0, w′(x)w′(x) exists, and the function w′(x)/w(x)w′(x)/w(x) is non-increasing on I  . Denote by ℓkℓk's the fundamental polynomials of Lagrange interpolation on a set of nodes x1