Lemma 2.17.
Assuming that:
A
⊆
𝔽
p
n
of density
α
ρ
>
0
𝟙
sup
t
≠
0
|
𝟙
A
^
(
t
)
|
≥
ρ
α
Then
there exists
V
≤
𝔽
p
n
of codimension
1
and
x
∈
𝔽
p
n
such that
|
A
∩
(
x
+
V
)
|
≥
α
(
1
+
ρ
2
)
|
V
|
.