On the Almost Everywhere Divergence of Lagrange Interpolatory Polynomials for Arbitrary System of Nodes

are the Lebesgue functions and Lebesgue constants of the interpolation, respectively . We now prove this statement in full detail . The detailed proof turned out to be quite complicated and several unsuspected difficulties had to be overcome . In the same paper P. Erdős also stated, that there is a pointgroup {x kn } so that for every continuous f (x) (-1 x:1) L,,(f, x,) -f (xo) holds for at least n one xo for which lim Z Ilk ,(xo) I = . This is perhaps true, but at this moment n-k=1 we cannot prove it (the original "proof" was probably incomplete) . We hope to settle it on another occasion .