Geodesic
On the Necessity of the Lindeberg Condition for the Normal Convergence of Martingales
Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 51-58

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We give conditions on square-integrable martingales whose consequence is the “conditional” Lindeberg condition. 
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     author = {V. M. Kruglov},
     title = {On the {Necessity} of the {Lindeberg} {Condition} for the {Normal} {Convergence} of {Martingales}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_1_a6/}
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V. M. Kruglov. On the Necessity of the Lindeberg Condition for the Normal Convergence of Martingales. Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 51-58. http://geodesic.mathdoc.fr/item/MZM_2001_70_1_a6/