%X We introduce and study a strengthening of the notion of stable convergence. %I Springer-Verlag %K Conditional distribution, Conditional expectation, Convergence in L1, Stable convergence, Central limit theorems %T A strong form of stable convergence %P 203-225 %B S?minaire de Probabilit?s XL %E Catherine Donati-Martin %E Michel ?mery %E Alain Rouault %E Christophe Stricker %O Lecture Notes in Mathematics, Volume 1899/2007, ISSN 0075-8434 %J S?minaire de Probabilit?s XL %D 2007 %S Lecture Notes in Mathematics %R doi:10.1007/978-3-540-71189-6_9 %L eprints983 %A Irene Crimaldi %A Giorgio Letta %A Luca Pratelli