Multifunctions of Souslin type
- 1 December 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 11 (3) , 395-411
- https://doi.org/10.1017/s0004972700044038
Abstract
LetSandXbe any two sets; then a mapping Γ which assigns to each pointtinSa set Γ(t) of points inXis called amultifunctionfromSintoX. Aselectorfor Γ is a functionffromSintoXsuch thatf(t)∈ Γ(t) for eacht. We introduce here a class of multifunctions which is both well-supplied with measurable selectors and yet is comprehensive enough to include those kinds of multifunction which have been most commonly studied before. Hence in order to show that a multifunction with non-empty values, which may arise naturally in an implicit function problem, has a measurable selector, it is sufficient to show that it is of Souslin type.Keywords
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