  De Finetti's betting argument is used to justify finitely additive
probabilities when only finitely many bets are considered. Under what
circumstances can countably many bets be used to justify countable additivity?
In this framework, one faces issues such as the convergence of the returns of
the bet. Generalizations of de Finetti's argument depend on what type of
conditions on convergence are required of the bets under consideration. Two new
such conditions are compared with others presented in the literature.
