Edward James McShane, mathematician

McShane was a very versatile applied mathematician. It was his direct definition of a stochastic integral, in classical probability, that is connected with our own work, in [86], 1987. In his book, Integration Theory, McShane is able to give a construction in which the integrater is not a martingale, but obeys suitable estimates, called "standing conditions". We are able to obtain a similar condition, and result, in quantum theory, while at the same time, sharpening the conclusion.