A result of Vapnik with applications

The proof offered of Theorem 2.1 of [2] is incorrect. The correct proof should follow that given in [l], as follows. With the notation as in [2], one first observes that @(z) v2”(R)< max __ rs. sm InI’where O (z)= I {z~/i: TZER}~. Fix ZESTY, and let Ai, Rt for 1< i< t be as in [2]. Noting that SZE R if and only if rz E R’for some i between 1 and t, one has O (z)< xi= 1 O’(z). The result follows on bounding O’(z) as in [2].