Kuhn's equivalence theorem for games in product form

We propose an alternative to the tree representation of extensive form games. Games in product form represent information with σ-fields over a product set, and do not require an explicit description of the play temporal ordering, as opposed to extensive form games on trees. This representation encompasses games with continuum of actions and imperfect information. We adapt and prove Kuhn's theorem — regarding equivalence between mixed and behavioral strategies under perfect recall — for games in product form with continuous action sets.