We prove that the class mc4 of continuous martingales with parameter set [0,1]2, bounded in L4, is included in the class of semi-martingales Sc8(L0(P)) defined by Allain in [A]. As a consequence we obtain a compact Itô's formula. Finally we relate this result with the compact Itô formula obtained by Sanz in [S] for martingales of mc4.
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