Measurability Is Not About Information

Information is not about measurability

We present a simple example where the use of σ-algebras as a model of information leads to a paradoxical conclusion: a decision maker prefers less information to more. We then explain that the problem arises because the use of σ-algebras as the informational content of a signal is inadequate. We provide a characterization of the different models of information in the literature in terms of Blac...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

A Puzzle about Laws, Symmetries and Measurability

I describe a problem about the relations among symmetries, laws andmeasurable quantities. I explain why several ways of trying to solve it will not work, and I sketch a solution that might work. I discuss this problem in the context of Newtonian theories, but it also arises for many other physical theories. The problem is that there are two ways of defining the space-time symmetries of a physic...

Information , measurability , and continuous behavior

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...

Quantum theory realises all joint measurability graphs

Joint measurability of sharp quantum observables is determined pairwise, and so can be captured in a graph. We prove the converse: any graph, whose vertices represent sharp observables, and whose edges represent joint measurability, is realised by quantum theory. This leads us to show that it is not always possible to use Neumark dilation to turn unsharp observables into sharp ones with the sam...