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Miklós Schweitzer
1984 Miklós Schweitzer
2
Miklós Schweitzer 1984- Problem 2
Miklós Schweitzer 1984- Problem 2
Source:
September 4, 2016
college contests
Problem Statement
2. Show that threre exist a compact set
K
⊂
R
K \subset \mathbb{R}
K
⊂
R
and a set
A
⊂
R
A \subset \mathbb{R}
A
⊂
R
of type
F
σ
F_{\sigma}
F
σ
such that the set
{
x
∈
R
:
K
+
x
⊂
A
}
\{ x\in \mathbb{R} : K+x \subset A\}
{
x
∈
R
:
K
+
x
⊂
A
}
is not Borel-measurable (here
K
+
x
=
{
y
+
x
:
y
∈
K
}
K+x = \{y+x : y \in K\}
K
+
x
=
{
y
+
x
:
y
∈
K
}
). (M.16) [M. Laczkovich]
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