The stability of optimal plans with respect to information is studied given the representation of information as sub-σ -fields of a probability space. A decision maker is constrained to choose a plan measurable with respect to her information. Continuity is derived by characterizing the continuity of the measurability constraint correspondence and then applying a generalized maximum theorem. Th...

Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.

We comment on the relation between models of information based on signals/partitions, and those based on σ-algebras. We show that more informative signals need not generate finer σ-algebras, hence that Blackwell’s theorem fails if information is modeled as σ-algebras. The reason is that the σ-algebra generated by a partition does not contain all the events that can be known from the information...

We show that the nondemolition measurement of a spacelike Wilson loop operator W(C) is impossible in a relativistic non-Abelian gauge theory. In particular, if two spacelike-separated magnetic flux tubes both link with the loop C, then a nondemolition measurement of W(C) would cause electric charge to be transferred from one flux tube to the other, a violation of relativistic causality. A destr...

The present work is a continuation of the previous papers written by the author on the subject. In terms of the measurability (or measurable quantities) notion introduced in a minimal length theory, first the consideration is given to a quantum theory in the momentum representation. The same terms are used to consider the Markov gravity model that here illustrates the general approach to studie...

We show that any finite-variance, isotropic random field on a compact group is necessarily meansquare continuous, under standard measurability assumptions. The result extends to isotropic random fields defined on homogeneous spaces where the group acts continuously. •