An important conjecture in the theory of Borel sets in non-separablemetric spaces is whether any point-countable Borel-additive family ina complete metric space has a $sigma$-discrete refinement. We confirm the conjecture forpoint-countable $mathbfPi_3^0$-additive families, thus generalizing results ofR. W. Hansell and the first author. We apply this result to theexistence of Borel measurable selectors for multivalued mappings oflow Borel complexity, thus answering in the affirmative a particularversion of a question of J. Kaniewski and R. Pol.
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