We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms.

中文翻译：

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强局部狄利克雷空间的 Rademacher 型定理和 Sobolev-to-Lipschitz 性质

我们广泛讨论了强局部狄利克雷空间上广义内在距离的 Rademacher 和 Sobolev-to-Lipschitz 性质，可能没有方场算子。我们展示了许多非光滑和无限维的例子。作为一个应用，我们证明了关于一大类强局部狄利克雷形式的给定距离函数的积分 Varadhan 短时渐近。