1982 Reports

Measuring Uncertainty Without a Norm

Werschulz, Arthur G.

Traub, Wasilkowski, and Wozniakowski have shown how uncertainty can be defined and analyzed without a norm or metric. Their theory is based on two natural and non-restrictive axioms. We show that these axioms induce a family of pseudometrics, and that balls of radius E are (roughly) the E-approximations to the solution. In addition, we show that a family of pseudometrics is necessary, even for the problem of computing x such that | f(x) | < E , where f is a real function.