Caratheodory Measurability

This open problem belongs to the area of game-theoretic probability.

  • In the protocol of the strong law of large numbers for bounded observations, upper probability is an outer measure in the sense of Caratheodory. What is the class of Caratheodory measurable sets with respect to this outer measure?
  • What is the class of sets for which upper probability coincides with lower probability?