We verify the existence of a purely unrectifiable set in which the typical Lipschitz function has a large set of full differentiability points. The example arises from a construction, due to Cs\"ornyei, Preiss and Ti\v{s}er, of a universal differentiability set in which a certain Lipschitz function has only a purely unrectifiable set of differentiability points.

中文翻译：

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极小的集合内的典型可微性

我们验证了一个纯粹不可修正的集合的存在，其中典型的 Lipschitz 函数具有大量的完全可微分点。由于 Cs\"ornyei、Preiss 和 Ti\v{s}er 的缘故，这个例子源于一个通用可微集的构造，其中某个 Lipschitz 函数只有一组纯粹不可校正的可微点。