Riemann-integration and a new proof of the Bichteler–Dellacherie theorem

We give a new proof of the celebrated Bichteler–Dellacherie theorem, which states that a process S is a good integrator if and only if it is the sum of a local martingale and a finite-variation process. As a corollary, we obtain a characterization of semimartingales along the lines of classical Riemann integrability.