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Let X be an analytic space (e.g., a complete metric space). We prove that any point-countable /"„-set cover of X either has a-discrete refinement, or else there is a compact subset of X not covered by any countable subfamily of the cover. It follows that any point-countable /^-additive family in X has a a-discrete refinement. This is used to show that any weakly immeasurable multimap, defined on X and taking nonempty, closed and separable values in a complete metric space, has a selector of the first Baire class.

𝐹_{𝜎}-set covers of analytic spaces and first class selectors