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Miklós Schweitzer
1995 Miklós Schweitzer
2
2
Part of
1995 Miklós Schweitzer
Problems
(1)
find interval where integral is half
Source: miklos schweitzer 1995 q2
10/2/2021
Given
f
,
g
∈
L
1
[
0
,
1
]
f,g\in L^1[0,1]
f
,
g
∈
L
1
[
0
,
1
]
and
∫
0
1
f
=
∫
0
1
g
=
1
\int_0^1 f = \int_0^1 g=1
∫
0
1
f
=
∫
0
1
g
=
1
, prove that there exists an interval I st
∫
I
f
=
∫
I
g
=
1
2
\int_I f = \int_I g=\frac12
∫
I
f
=
∫
I
g
=
2
1
.
real analysis
calculus
integration
Miklos Schweitzer
college contests