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Miklós Schweitzer
1960 Miklós Schweitzer
8
8
Part of
1960 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1960- Problem 8
Source:
11/21/2015
8. Let
f
f
f
be a bounded real function defined on the unit cube
H
H
H
of the
n
n
n
-dimensional space and, for a given
y
y
y
, let
A
y
A_y
A
y
and
B
y
B_y
B
y
denote the parts of the interior of
H
H
H
on which
f
>
y
f>y
f
>
y
and
f
<
y
f<y
f
<
y
, respectively. Show that
f
f
f
is integrable in the Riemannian sense if and only if for every
y
y
y
almost all points of
A
y
A_y
A
y
and
B
y
B_y
B
y
are inner points. (R. 9)
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