**Mark J. Schervish, Teddy Seidenfeld and Joseph B. Kadane**

We extend a result of Dubins (1975) from bounded to unbounded random
variables. Dubins showed that a finitely additive
expectation over the collection of bounded random variables can
be written as an
integral of conditional expectations (disintegrability) if and only if
the marginal expectation is always within the smallest closed interval
containing the conditional expectations (conglomerability). We give a
sufficient condition to extend this result to the collection *Z* of
all random variables that have finite expected value and whose
conditional expectations are finite and have finite expected value. The
sufficient condition also allows the result to extend some, but not
all, subcollections of *Z*. We give an
example where the equivalence of disintegrability and conglomerability
fails for a subcollection of *Z* that still contains all bounded random
variables.

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