Reply to Letters of M. Tanemura and E. M. Tory and D. K. Pickard

Abstract

Yours sincerely, MOTooHoRI I regard the arguments of [2] to be heuristic, non-rigorous and hence incomplete. M. Tanemura's comments on Lemma 3 of [2] are well taken. In fact, it may be shown by comparison of M (x) with linear solutions to the basic integral equation for M(x) in the one-dimensional Renyi model ([2], p. 803, Equation (1.2» that for a~3a, (2.7a) of [2] should read (1) are decreasing. Similarly, the other ratio results of Lemma 3 of [2], p. 806 should be correspondingly changed. For example, (2.8a) should read (2) __ M-,,(~a,--, b__ )_< M(c, d) for (aa)(b -(3)= (c -a)(d -(3) a~c~a, b~d~{3.