Some results about multimeasures and their selectors

Radon-Nikodým theorems for multimeasures and transition multimeasures

“…In order to do this, we will need two results about transition measures and multimeasures that are actually of independent interest. [14], and also extends Theorem 5 of Godet-Thobie [12]. Proposition 4.2.…”

“…So let fm -^ / in L [X). From Theorem l(ii) of Godet-Thobie [12], we know that SM is w(ca(X), S ® X*)-compact.…”

“…From Theorem 1 of Godet-Thobie [12] (see also Theorem 2.3 of Hiai [14]), we know that, for all co € Cl, RA(co) ^ 0.…”

“…Depending on the way we interpret this equality of sets, we get different types of multimeasures. However, they all coincide when M(-) is ZJU)ytc(A')-valued (see Proposition 3 of GodetThobie [12] and Pallu de la Barriere [17]). This fact is the set valued analogue of the well known Orlicz-Pettis theorem (see, for example, Diestel-Uhl [8]).…”

“…Since then the subject of multimeasures has been developed extensively. Important contributions were made, among others, by Artstein [1], Costé [4,5], Costé-Pallu de la Barriere [6], Debreu-Schmeidler [7], Drewnowski [10], Godet-Thobie [12], Hiai [14] and Pallu de la Barriere [17].…”