Casella & Berger (2001) write:
the Axiom of Countable Additivity, is not universally accepted among statisticians. ... [It] is rejected by a school of statisticians led by deFinetti (1972), who chooses to replace this axiom with the Axiom of Finite Additivity.
What might possibly be wrong or objectionable about the Axiom of Countable Additivity?
(Simple examples would be helpful!)
The Axiom of Countable Additivity is the 3rd condition below:
from Hot Weekly Questions - Mathematics Stack Exchange
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