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Measure, Integration & Real Analysis
· Problem 2C.1
Measures — Sheldon Axler
Mathematics — Measure Theory · measures
Problem
Explain why there does not exist a measure space
(
X
,
S
,
μ
)
(X, \mathcal{S}, \mu)
(
X
,
S
,
μ
)
with the property that
{
μ
(
E
)
:
E
∈
S
}
=
[
0
,
1
)
\{\mu(E) : E \in \mathcal{S}\} = [0, 1)
{
μ
(
E
)
:
E
∈
S
}
=
[
0
,
1
)
.
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