In discrete time a local martingale is a martingale under an equivalent probability measure

1 Result and Discussion We consider a discrete-time infinite horizon model with an adapted d-dimensional process S = (S t) given on a stochastic basis (Ω, F, F = (F t) t=0,1,... , P). The notations used: M(P), M loc (P) and P are the sets of d-dimensional martingales, local martingales and predictable (i.e. (F t−1)-adapted) processes; H · S t = j≤t H j ∆S j. To our knowledge, this result was never formulated explicitly. On the other hand, it is well-known that if the stopped process S T = (S t∧T), T ∈ N, belongs to M loc (P) then there exists˜P T ∼ P (and even with bounded density d ˜ P T /dP) such that S T ∈ M(˜ P T). This assertion is contained in the classical DMW criteria of absence of arbitrage, see the original paper [1] by Dalang– Morton–Willinger and more recent presentations in [3] and [4] with further references wherein. So, the news is: if S ∈ M loc (P) then the intersection of the sets of true martingale measures for the processes S T is non-empty. Theorem 1 can be extracted from the old paper [6] by Schachermayer which merits a new reading. The proof given here uses the same approach of geometric functional analysis as in [6]. It is based on separation arguments