  The class of location-scale finite mixtures is of enduring interest both from
applied and theoretical perspectives of probability and statistics. We prove
the following results: to an arbitrary degree of accuracy, (a) location-scale
mixtures of a continuous probability density function (PDF) can approximate any
continuous PDF, uniformly, on a compact set; and (b) for any finite $p\ge1$,
location-scale mixtures of an essentially bounded PDF can approximate any PDF
in $\mathcal{L}_{p}$, in the $\mathcal{L}_{p}$ norm.
