Let E be a set on the unit circle T of \(\mathbb C\). We prove that there exists an \(f \in H^\infty \) which has no radial limits on E but has unrestricted limit at each point of \(T {\setminus } E\) if and only if E is an \(F_\sigma \) of measure zero. The necessity of the condition that E is an \(F_\sigma \) is almost obvious and the necessity of the condition that E is of measure zero follows from Fatou’s theorem.

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关于法头定理

设E为\（\ mathbb C \）的单位圆T上的集合。我们证明存在一个\（f \ in H ^ \ infty \），它对E没有径向限制，但在且仅当E为\\时，在\（T {\ setminus} E \）的每个点都具有不受限制的限制。 （F_ \ sigma \）测量为零。该条件的必要性是Ë是\（F_ \西格玛\）几乎是显而易见的，而且条件的必要性Ë是衡量为零从法图定理如下。