Abstract
We extend to higher dimensions a theorem of Lusin and Privalov concerning radial limit zero sets of holomorphic functions on the unit disc, and we show that, in contrast to the case in dimension one, the converse fails for holomorphic functions on the unit ball in . Finally, we show that in higher dimensions any characterization of the radial limit zero sets of holomorphic functions on the ball must take into account the ‘complex structure’ on the sphere.
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