Abstract. By the observation that every almost monotone non-increasing sequence $\{a_n\} $ has the same convergence and divergence property as the monotone non-increasing sequence $\{\alpha_n\}, \alpha_n:=\sup_{k\ge n}a_k,$ we can slightly weaken the assumptions on the coefficients of Tandori's divergence theorems from monotonicity to almost monotonicity.

AMS Subject Classification (1991): 42C15, 42C05

Received January 20, 2003. (Registered under 2893/2009.)