In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special functions of bounded variation, without adding significant jumps. As a main tool, we study the variational 1-capacity and its BV analog.

中文翻译：

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在度量空间中通过 SBV 函数逼近 BV

在配备加倍测度并支持 Poincar\'e 不等式的完整度量空间中，我们证明了有界变差函数（BV 函数）可以通过有界变差的特殊函数在严格意义上和逐点一致地近似，而无需添加显着的跳跃。作为主要工具，我们研究了变分 1-容量及其 BV 模拟。