On non-injectivity of Borel functions selecting points from compact sets

We show that no Borel function on the hyperspace of a compact metric space X, selecting points from nonempty closed sets in X, can be injective on a r esidual set in the hyperspace. As a consequence, we show that a measure-the oretic analogue of the marriage theorem for finite sets, obtained by R. D. Mauldin [7], [3], fails in the Baire category setting. This answers a quest ion from [1].