Infinite Sum Theorem

Let h(x, y, z) be continuous on an open region E₀ and let B be a function which assigns a real number B(E) to each region E contained in E₀. Assume that:

(i) B has the Addition Property.

(ii) B(E) ≥ 0 for every E.

(iii) For every element of volume ΔE,

B(ΔE) ≈ h(x, y, z) ΔV (compared to ΔV),

Then