On the measurability of functions with quasi-continuous and upper semi-continuous vertical sections

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