We show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if
(
X
,
d
,
μ
)
(X,d,\mu )
is a locally complete and separable metric measure space, then continuous functions are dense in the Newtonian space
N
1
,
p
(
X
)
N^{1,p}(X)
. Here the measure
μ
\mu
is Borel and is finite and positive on all metric balls. In particular, we don’t assume properness of
X
X
, doubling of
μ
\mu
or any Poincaré inequalities. These resolve, partially or fully, questions posed by a number of authors, including J. Heinonen, A. Björn and J. Björn. In contrast to much of the past work, our results apply to locally complete spaces
X
X
and dispenses with the frequently used regularity assumptions: doubling, properness, Poincaré inequality, Loewner property or quasiconvexity.