Full support of Riemannian volume #
The Riemannian volume measure of a continuous finite-dimensional Riemannian manifold is positive on nonempty open sets. This gives the full-support interface used by later integration and positivity arguments.
instance
TauCeti.isOpenPosMeasure_riemannianVolume
{E : Type u_1}
[NormedAddCommGroup E]
[NormedSpace ℝ E]
[FiniteDimensional ℝ E]
{H : Type u_2}
[TopologicalSpace H]
{I : ModelWithCorners ℝ E H}
{M : Type u_3}
[TopologicalSpace M]
[ChartedSpace H M]
[IsManifold I 1 M]
[MeasurableSpace M]
[BorelSpace M]
[LindelofSpace M]
[Bundle.RiemannianBundle fun (x : M) => TangentSpace I x]
[IsContinuousRiemannianBundle E fun (x : M) => TangentSpace I x]
:
Riemannian volume is positive on every nonempty open set.