Abstract
We prove universal compact-measurability of the intersection of a compact-measurable Souslin family of closed-valued multifunctions. This generalizes previous result on intersections of measurable multifunctions. We introduce the unique maximal part of a multifunction which is defined on the quotient given by an equivalence relation. Measurability of this part of a multifunction is proven in a special case. We show how these results apply to the spectral theory of measurable families of closed linear operators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bourbaki N.,Elements of Mathematics: General Topology, Part I and II. Springer, (1974), 1989.
Castaing C., Valadier M.,Convex Analysis and measurable Multifunctions. Springer, 1977.
Himmelberg C. J., Parthasarathy T., Van Vleck F. S.,On measurable relations. Fund. Math.,111 (1981), 161–167.
Kechris A. S.,Classical Descriptive Set Theory. Springer, 1995.
Pastur L. A., Figotin A.,Spectra of Random and Almost-Periodic Operators. Springer, 1992.
Spakowski A., Urbaniec P.,On measurable multifunctions in countably separated spaces. Rend. Circ. Mat. Palermo, Serie II,42 (1993), 82–92.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Taraldsen, G. Measurability of intersections of measurable multifunctions. Rend. Circ. Mat. Palermo 45, 459–472 (1996). https://doi.org/10.1007/BF02844516
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02844516