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IV: 03, 37-46, LNM 124 (1970)
CHERSI, Franco
Martingales et intégrabilité de $X\log^+X$ d'après Gundy (Martingale theory)
Gundy's result (Studia Math., 33, 1968) is a converse to Doob's inequality: for a positive martingale such that $X_n\leq cX_{n-1}$, the integrability of $\sup_n X_n$ implies boundedness in $L\log^+L$. All martingales satisfy this condition on regular filtrations
Comment: The integrability of $\sup_n |\,X_n\,|$ has become now the $H^1$ theory of martingales
Keywords: Inequalities, Regular martingales
Nature: Exposition, Original additions
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