Asymptotic equivalence of uniform Riemann sums and infinite-limit Riemann sums

Let a continuous curve be given, and consider a uniform Riemann sum for it together with a Riemann sum whose limit is infinite. Asymptotic equivalence conjecture. A uniform Riemann sum of a continuous curve is asymptotic to a Riemann sum with infinite limit. This conjecture concerns the relationship between finite uniform Riemann sums and Riemann sums in the paper's two-tiered calculus involving infinite limits; the supplied text does not establish whether the assertion is known or resolved.