infinitevolume
In mathematics, infinite volume describes a space or region whose volume, defined by a standard measure such as Lebesgue measure, is infinite. In Euclidean space R^n, the volume of a measurable set E is Vol(E) ∈ [0, ∞], and Vol(E) = ∞ when the measure does not converge. Some familiar infinite-volume regions include the whole space R^n, a half-space, or an infinite cylinder. By contrast, some unbounded regions can have finite volume; for example, the Gabriel’s horn, formed by revolving y = 1/x for x ≥ 1 about the x-axis, has finite volume despite infinite extent.
Volume depends on the chosen measure and geometry. In general metric measure spaces, infinite volume means
In differential geometry, a Riemannian manifold can have finite or infinite volume. Euclidean space has infinite
In physics, the infinite-volume limit or thermodynamic limit refers to taking the size of a system to