Foundations of the theory of probability

68 VI. Independence;TheLawofLargeNumbers

Theninorderthatseries

(

1

) convergewiththeprobabilityone,

itisnecessaryandsufficient

10

thatthefollowingseriesconverge

simultaneously

:

CO CO

CO

Z

p

(W>1}. Z

E

(%.)

and

2>

2

(y„)

n=l n=l

n=l

10

Cf.A.KhintchineandA.Kolmogorov, OntheConvergence

of

Series,

Rec.Math.Soc.Moscow,v.
32,1925,p.

668-677.