  We establish a verification theorem, inspired by those existing in stochastic
control, to demonstrate how a pair of progressively measurable controls can
form a Nash equilibrium in a stochastic zero-sum differential game.
Specifically, we suppose that a pathwise-type Isaacs condition is satisfied
together with the existence of what is termed a quasi-strong solution to the
Bellman-Isaacs (BI)equations. In that case we are able to show that the value
of the game is achieved and corresponds exactly to the unique solution of the
BI equations. Those have also been applied for improving a well-known
verification theorem in stochastic control theory. In so doing, we have
implemented new techniques of stochastic calculus via regularizations,
developing specific chain rules.
