Volumeen
Volumeen is a term used in some mathematical discussions to denote a generalized volume measure that incorporates a spatially varying density. It serves as a weighted analog of ordinary volume, allowing regions to contribute to the measure in proportion to a density function.
Formally, let D be a measurable subset of R^n and let ρ: R^n → [0, ∞) be a measurable
Properties of volumeen include nonnegativity, monotonicity (D1 ⊆ D2 implies Vol_en(D1) ≤ Vol_en(D2)), and additivity over disjoint unions.
Applications span probability and statistics (volumeen of a region under a density equals probability mass), computer
Computation can be analytic for simple regions and densities; otherwise numerical integration, quadrature, or Monte Carlo
See also: measure, volume, density function, weighted measure, voxel, Monte Carlo integration.