Theorem 3.1
(Khintchine’s inequality)
.
Assuming that:
p
∈
[
2
,
∞
)
X
1
,
X
2
,
…
,
X
n
independent random variables
ℙ
(
X
i
=
x
i
)
=
1
2
=
ℙ
(
X
i
=
−
x
i
)
Then
∥
∑
i
=
1
n
X
i
∥
L
p
(
ℙ
)
=
O
(
p
1
2
(
∑
i
=
1
n
∥
X
i
∥
L
2
(
ℙ
)
2
)
1
2
)
.