The error on a real quantity Y due to the graduation of the measuring
instrument may be represented, when the graduation is regular and fines down,
by a Dirichlet form on R whose square field operator do not depend on the
probability law of Y as soon as this law possesses a continuous density. This
feature is related to the "arbitrary functions principle" (Poincar\'{e}, Hopf).
We give extensions of this property to multivariate case and infinite
dimensional case for approximations of the Brownian motion. We use a Girsanov
theorem for Dirichlet forms which has its own interest. Connections are given
with discretization of stochastic differential equations.Comment: 23
