In this article, we discuss the stability of the Nagaoka state with an
infinite number of holes in the infinite-U Hubbard model. We shall ri
gorously show that the Nagaoka state is stable if the total number of
holes N(h) almost-equal-to N(LAMBDA)alpha with 0 less-than-or-equal-to
alpha < 2/(d+2) as the number of lattice sites N(LAMBDA) tends to inf
inity. Our theorem improves greatly the previous results obtained by B
arbieri et al. [Phys. Rev. B 41 (1990) 11697] and by Tian [Phys. Rev.
B 44 (1991) 4444].