Theorem 3.9
(Bogolyubov again, after Sanders)
.
Assuming that:
A
⊆
𝔽
p
n
of density
α
>
0
Then
there exists a subspace
V
≤
𝔽
p
n
of codimension
O
(
log
4
α
−
1
)
such tht
V
⊆
A
+
A
−
A
−
A
.