ABSTRACT
A differential a on K is d am pab le if ua is absolutely inte g ra te for some damper u on K . a is dam per-sum m ab le if ua is summable for some damper u on K . That is, u\a\ < τ for some damper u and some integrable r on K . (See Theorem 2, §2.5.) A summant «S' on i f is ta m e if u\S\ < T for some damper u and some additive summant T on K . σ is dampersummable if and only if a — [5] for some tame S. (This is the equivalence of (i) and (iii) in Exercise 15.)
Clearly every dampable differential is damper-summable, as is every summable differential. But not every summable dif ferential is dampable, as the following example shows.
