We give the following version of Fatou's theorem for distributions that are boundary values of analytic functions. We prove that if $finmathcal{D}^{prime}left(a,bight) $ is the distributional limit of the analytic function $F$ defined in a region of the form $left(a,bight)imesleft( 0,Right),$ if the one sided distributional limit exists, $fleft(x_{0}+0ight)=gamma,$ and if $f$ is distributionally bounded at $x=x_{0},$ then the Lojasiewicz point value exists, $fleft(x_{0}ight)=gamma$ distributionally, and in particular $F(z)ogamma$ as $zo x_{0}$ in a non-tangential fashion.
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机译：对于分布是分析函数的边界值的分布，我们给出了法图定理的以下形式。我们证明如果$ f in mathcal {D} ^ { prime} left（a，b right）$是在形式$ left（ a，b right） times left（0，R right），$如果存在单侧分布限制，则$ f left（x_ {0} +0 right）= gamma，$并且$ f $的分布边界为$ x = x_ {0}，$然后存在Lojasiewicz点值，$ f left（x_ {0} right）= gamma $分布，特别是$ F（z） to 以非切线方式将gamma $作为$ z 到x_ {0} $。
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