We prove the continuity of the mappings with finite distortion of the Sobolev class \( W^{1}_{\nu,\operatorname{loc}} \) on Carnot groups and establish that these mappings are \( \mathcal{P} \)-differentiable almost everywhere and have the Luzin \( \mathcal{N} \)-property.

中文翻译：

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卡诺群上 Sobolev 类 $ W^{1}_{\nu,\operatorname{loc}} $ 有限畸变映射的连续性

我们证明了卡诺群上 Sobolev 类\( W^{1}_{\nu,\operatorname{loc}} \)的有限失真映射的连续性 ，并确定这些映射是\( \mathcal{P} \) -几乎处处可微，并具有 Luzin \( \mathcal{N} \) -性质。