where
denotes the expectation value of restricted to outcomes , then the Lindeberg condition is
(4)
for all
(Zabell 1995).
In the terminology of Feller (1971), the Lindeberg condition assumed that for each ,
(5)
or equivalently
(6)
Then the distribution
(7)
tends to the normal distribution with zero expectation and unit variance (Feller 1971, p. 256). The Lindeberg condition
(5) guarantees that the individual variances are small compared to their sum in the sense that for given for all sufficiently
large ,
for ,
...,
(Feller 1971, p. 256).
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