ABSTRACT. Let f : R 2 → R be a function with upper semicontinuous and quasi-continuous vertical sections f x (t) = f (x, t), t, x ∈ R. It is proved that if the horizontal sections f y (t) = f (t, y), y, t ∈ R, are of Baire class α (resp. Lebesgue measurable) [resp. with the Baire property] then f is of Baire class α + 2 (resp. Lebesgue measurable and sup-measurable) [resp. has Baire property].
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