Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces

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The BV-capacity in metric spaces (2010, background): “The functions in N(X) with 1 ≤ p < ∞ are necessarily p-quasicontinuous (see [5] and [3]) and thus the above definition of the capacity agrees with the definition of the Sobolev 1-capacity where the functions are required to satisfy u = 1 only in E.”
Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology (2012, background): “On metric spaces, such capacities have been used and studied under various assumptions by e.g. Heinonen–Koskela [22], Kallunki–Shanmugalingam [23] and Adamowicz–Björn–Björn–Shanmugalingam [1].”
Prime ends for domains in metric spaces (2012, unknown): “1 in Björn–Björn–Shanmugalingam [14] (or Lemma 5.”