Theorem 1.12
(Freiman-Ruzsa)
.
Assuming that:
A
⊆
𝔽
p
n
|
A
+
A
|
≤
K
|
A
|
(i.e.
σ
(
A
)
≤
K
)
Then
A
is contained in a subspace
H
≤
𝔽
p
n
of size
|
H
|
≤
K
2
p
K
4
|
A
|
.