Smoothness of the green function for some special compact sets

Smoothness of the Green functions for some special compact sets, which are sequences of closed intervals with certain parameters, is described in terms of the function ϕ(δ) = 1 log 1 δ that gives the logarithmic measure of sets. As a tool, we use the so-called nearly Chebyshev polynomials and Lagrange interpolation. Moreover, some concepts of potential theory are explained with illustrative examples.