Additive families of low Borel classes and Borel measurable selectors

Abstract

We show that point-countable F-sigma-delta-additive family of subsets of an absolutely Suslin space is sigma-discretely refinable. This generalizes a theorem of R.W.

Hansell. We apply this result on the existence of Borel measurable selectors for multivalued mappings of low Borel complexity, answering thus affirmatively a particular version of a question of J.

Kaniewski and R. Pol.

Keywords

• additive families
• Borel measurability
• selectors