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Infinite Sum Theorem
INFINITE SUM THEOREM Let h(x, y) be continuous on an open region D_{0} and let B be a function which assigns a real number B(D) to each region D contained in D_{0}. Assume that
Then We shall use the notation ΔB = B(ΔD). Given (i) and (ii), the theorem shows that if we always have ΔB ≈ h(x, y) ΔA (compared to ΔA) then B(D) ≈ ∑∑_{D }h(x, y) ΔA. The proof is simplest in the case that D is a rectangle.


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