Probabilities on streams and reflexive games

In this paper probability measures on streams (e.g. on hypernumbers and p-adic numbers) are defined. Then it is shown that these probabilities can be used for simulations of reflexive games. In particular, it can be proved that Aumann's Agreement Theorem does not hold for these probabilities. Instead of this theorem, there is a statement that is called the Reflexion Disagreement Theorem. Based on this theorem, probabilistic and knowledge conditions can be defined for reflexive games at different reflexion levels up to the infinite level.