Survey of Measurable Selection Theorems

Wagner, Daniel H.

doi:10.1137/0315056

Cited by 497 publications

(214 citation statements)

References 101 publications

Supporting

Mentioning

212

Contrasting

Order By: Relevance

“…Proof. Since B is an analytic subset oi T X X, it follows from the von NeumannYankov theorem (see [15]) that there is a sequence {g"}^=, of maps of T into X each of which is <S6B(F)-measurable and such that for each t, {g"(0: n E N} is dense in B,.…”

Section: Proof It Can Be Checked That H Satisfies Condition (1) Assmentioning

confidence: 99%

Measurable Representations of Preference Orders

Mauldin¹

1983

Transactions of the American Mathematical Society

View full text Add to dashboard Cite

Abstract. A continuous preference order on a topological space Y is a binary relation < which is reflexive, transitive and complete and such that for each x, {y: x < y) and {y: y < x) are closed. Let Tand Xbe complete separable metric spaces. For each t in T, let B, be a nonempty subset of X, let >} is a Borel set. Let B = ((t, x):x e B,}. Theorem 1. There is an ¡$(T) ^(Xymeasurable map g from B into R so that for each t, g(t, ) is a continuous map of B, into R and g(t, x) =ï g(T) forms the C-sets of Selivanovskii and ( X) is a Borel field on X.) Theorem 2. If for each t, B, is a a-compact subset of Y, then the map g of the preceding theorem may be chosen to be Borel measurable.The following improvement of a theorem of Wesley is proved using classical methods.Theorem 3. Let g be the map constructed in Theorem 1. If' ¡lis a probability measure defined on the Borel subsets of T, then there is a Borel set N such that fi(N) = 0 and such that the restriction of g to B D ((T -N) X X) is Borel measurable.

~~show abstract~~

Section: Proof It Can Be Checked That H Satisfies Condition (1) Assmentioning
confidence: 99%

Measurable Representations of Preference Orders
Mauldin¹
1983
Transactions of the American Mathematical Society
3
2
15
0
View full text Add to dashboard Cite

~~show abstract~~

“…The study of random fixed point theory was initiated by the Prague school of Probabilities in the 1950s [9,10,24]. Common random fixed point theorems are stochastic generalization of classical common fixed point theorems.…”

Section: Introductionmentioning
confidence: 99%

Some common random fixed point theorems for contractive type conditions in cone random metric spaces
Saluja¹,
Tripathi²
2016
Acta Universitatis Sapientiae, Mathematica
4
1
8
0
View full text Add to dashboard Cite

~~show abstract~~

“…For Py(X)-valued multifunctions, measurability implies graph measurability, while the converse is true if there is a <r-finite measure fi(-) on (Q, £), with respect to which £ is complete. For more details we refer to the survey paper of Wagner [15]. By Sf(l^p^oo) we will denote the set of selectors of F() that belong in the Lebesgue-Bochner space LP(X); i.e.…”

Section: Preliminariesmentioning
confidence: 99%

Continuous dependence results for a class of evolution inclusions
Papageorgiou¹
1992
Proceedings of the Edinburgh Mathematical Society
18
0
22
0
View full text Add to dashboard Cite

In this paper we examine the dependence of the solutions of an evolution inclusion on a parameter X. We prove two dependence theorems. In the first the parameter appears only in the orientor field and we show that the solution set depends continuously on it for both the Vietoris and Hausdorff topologies. In the second the parameter appears also in the monotone operator. Using the notion of G-convergence of operators we prove that the solution set is upper semicontinuous with respect to the parameter. Both results make use of a general existence theorem which we also prove in this paper. Finally, we present two examples. One from control theory and the other from partial differential inclusions.

~~show abstract~~

Survey of Measurable Selection Theorems

Cited by 497 publications

References 101 publications

Measurable Representations of Preference Orders

Measurable Representations of Preference Orders

Some common random fixed point theorems for contractive type conditions in cone random metric spaces

Continuous dependence results for a class of evolution inclusions

Contact Info

Product

Resources

About