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Miklós Schweitzer
2006 Miklós Schweitzer
8
8
Part of
2006 Miklós Schweitzer
Problems
(1)
measurablility of level sets
Source: Miklos Schweitzer 2006 q8
9/14/2021
let
f
(
x
)
=
∑
n
=
0
∞
2
−
n
∣
∣
2
n
x
∣
∣
f(x) = \sum_{n=0}^{\infty} 2^{-n} ||2^n x||
f
(
x
)
=
∑
n
=
0
∞
2
−
n
∣∣
2
n
x
∣∣
, where ||x|| is the distance between x and the closest integer to x. Are the level sets
{
x
∈
[
0
,
1
]
:
f
(
x
)
=
y
}
\{ x \in [0,1] : f(x)=y \}
{
x
∈
[
0
,
1
]
:
f
(
x
)
=
y
}
Lebesgue measurable for almost all
y
∈
f
(
R
)
y \in f(R)
y
∈
f
(
R
)
?
real analysis