Flatness of distributions vanishing on infinitely many hyperplanes (Q1046533)

The author considers an infinite family \(\{L_k\}^{\infty}_{k=1} \) of hyperplanes in \(\mathbb R^n\) and a limiting hyperplane \( L _{0}\) of \({L_k}\). Let \(u\) be an infinitely differentiable function vanishing on \({ L_k}\cap{U}\) for all \(k\geqslant 1\), where \( U\) is an open set in \(\mathbb R ^n \) intersecting of \( L _{0}\). Then \(u\) must be flat at \( L _{0}\) .