Abstract. This paper shows that optimal Lebesgue function type sum $\Lambda_n(\chi ^*,x)$ must equioscillate and gives the optimal set of nodes and the exact value of $\lambda_n(s)$.

AMS Subject Classification (1991): 41A05

Received October 25, 1996 and in revised form May 7, 1997. (Registered under 5779/2009.)