In this article, at page 120, the author states that
the question was solved for three random points forming a spherical triangle on the n-dimensional sphere.[...]since the sphere is compact, then points can be generated randomly on the sphere with all points being equally likely.
However, is there any justification for why we can generate random point on a compact set (in this case a subset of Euclidean space) with all point being equally likely ? (whereas if this is not the case, we cannot)