A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example,
implies
for any .
The converse is false, but can be made into a correct Tauberian
theorem if
is subjected to an appropriate additional condition (Hardy 1999, p. 46).
.
The converse is false, but can be made into a correct Tauberian
theorem if 
is subjected to an appropriate additional condition (Hardy 1999, p. 46).
