Finitely Additive FTAP under an Atomic Reference Measure

Let L be a linear space of real bounded random variables on the probability space (Ω,,P0) . A finitely additive probability P on  such that P∼P0 and EP(X)=0 for each X∈L is called EMFA (equivalent martingale finitely additive probability). In this note, EMFA’s are investigated in case P 0 is atomic. Existence of EMFA’s is characterized and various examples are given. Given y ∈ ℝ and a bounded random variable Y, it is also shown that Xn+y⟶a.s.Y , for some sequence (X n ) ⊂ L, provided EMFA’s exist and E P (Y) = y for each EMFA P.