In outline, the argument follows that of the single-valued setting, but there are several significant issues that must be addressed in the $n$-valued case.
The proof makes use of many of the ideas of the general case, but in a simpler setting.
[3] contains an extension of Proposition 2 to the setting of finitely additive set functions.
The point is that the operator is now much easier to analyse than is the case in the original setting of the space $B$.
It seems that the relations between these concepts emerge most clearly when the setting is quite abstract, and this (rather than a desire for mere generality) motivates our approach to the subject.
Here the functional analytic tools required are simpler, but this easier setting allows us to develop some methods without undue worry about technicalities.
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