Measure in cosmology: convention versus paradox

Commentator: Pieter Thyssen, UCLouvain

Résumé: Standard probability theory is restricted to real-valued measures that are non-negative, normalized, and countably additive. Normality is a convention added to the requirement of being non-zero and bounded. The countably additivity axiom was introduced by Kolmogorov for mathematical convenience. Together, normality and countable additivity ensure countable conglomerability, which guarantees that the probability of a given event lies in the range of probabilities of that event conditional on all members of any countable partition. In cosmological models with infinite phase spaces, however, the conventions inherent to standard probability measures may lead to formal inconsistencies. In this talk, we explore the paradoxes as well as some alternative approaches, all of which allow for failures of countable conglomerability.