Strong Asymptotics for Extremal Polynomials Associated with Weights on ℝ 0. The results are consequences of a strengthened form of the following assertion: Given 0 <p1. Auxiliary results include inequalities for weighted polynomials and zeros of extremal polynomials. The monograph is fairly self contained with proofs involving elementary complex analysis and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials