CFDP 1296

Measurability Is Not about Information

Author(s): 

Publication Date: March 2001

Pages: 11

Abstract: 

We comment on the relation between models of information based on signals/partitions, and those based on sigma-algebras. We show that more informative signals need not generate finer sigma-algebras, hence that Blackwell’s theorem fails if information is modeled as sigma-algebras. The reason is that the sigma-algebra generated by a partition does not contain all the events that can be known from the information provided by the signal. We also show that there is a non-conventional sigma-algebra that can be associated to a signal which does preserve its information content. Further, expectations and conditional expectations may depend on the choice of sigma-algebra that is associated to a signal. We provide a simple characterization of when the model is robust to changes in the sigma-algebras.

Keywords: 

Blackwell’s theorem, measurability, models of information, partitions, information-preserving sigma-algebras

JEL Classification Codes:  C60, C70, G12