  We propose an alternative to the tree representation of extensive form games.
Games in product form represent information with $\sigma$-fields over a product
set, and do not require an explicit description of the play temporality, as
opposed to extensive form games on trees. This representation encompasses games
with a continuum of actions, randomness and players, as well as games for which
the play order cannot be determined in advance. 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.
