Riemann-measurable selections. (English) Zbl 0851.54021

Saint Raymond, Jean

Set-Valued Anal. 2, No. 3, 481-485 (1994).

Summary: Let \(X\) be a Polish space equipped with a \(\sigma\)-finite regular Borel measure \(\mu\). If \(E\) is a metric space and \(F\) a set-valued function: \(X\to 2^E\) with complete values, and if \(F\) is lower semicontinuous at almost all points of \(X\), we prove that there exists a Riemann-measurable selection \(s\) of \(F\).

MSC:

54C65	Selections in general topology
54C60	Set-valued maps in general topology

Keywords:

Riemann-measurable selection

References:

[1]	Michael, E.: Continuous selections II,Ann. of Math. 64 (1956), 562-580. · Zbl 0073.17702 · doi:10.2307/1969603
[2]	Jayne, J.E. and Rogers, C.A.: Upper semicontinuous set-valued functions,Acta Math. 149 (1982), 87-125. Correction155 (1985), 149-152. · Zbl 0523.54013 · doi:10.1007/BF02392351
[3]	Jayne, J.E. and Rogers, C.A.: Borel selectors for upper semicontinuous multi-valued functions,J. Funct. Anal. 56 (1984), 279-299. · Zbl 0581.28007 · doi:10.1016/0022-1236(84)90078-8
[4]	Jayne, J.E. and Rogers, C.A.: Borel selectors for upper semicontinuous set-valued maps,Acta Math. 155 (1985), 41-79. · Zbl 0588.54020 · doi:10.1007/BF02392537
[5]	Hansell, R. W.: First class selectors for upper semi-continuous multifunctions,J. Funct. Anal. 75 (1987), 382-395. · Zbl 0644.54014 · doi:10.1016/0022-1236(87)90102-9
[6]	Hansell, R.W., Jayne, J.E. and Talagrand, M.: First class selectors for weakly upper semi-continuous multivalued maps in Banach spaces,J. Reine Angew. Math. 361 (1985), 201-220. Correction362 (1986), 219-220. · Zbl 0573.54012