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Measure, Integration & Real Analysis
· Problem 2C.4
Measures — Sheldon Axler
Mathematics — Measure Theory · measures
Problem
Give an example of a measure space
(
X
,
S
,
μ
)
(X, \mathcal{S}, \mu)
(
X
,
S
,
μ
)
such that
{
μ
(
E
)
:
E
∈
S
}
=
{
∞
}
∪
⋃
k
=
0
∞
[
3
k
,
3
k
+
1
]
.
\{\mu(E) : E \in \mathcal{S}\} = \{\infty\} \cup \bigcup_{k=0}^{\infty} [3k, 3k+1].
{
μ
(
E
)
:
E
∈
S
}
=
{
∞
}
∪
k
=
0
⋃
∞
[
3
k
,
3
k
+
1
]
.
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