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Measure, Integration & Real Analysis
· Problem 2C.6
Measures — Sheldon Axler
Mathematics — Measure Theory · measures
Problem
Find all
c
∈
[
3
,
∞
)
c \in [3, \infty)
c
∈
[
3
,
∞
)
such that there exists a measure space
(
X
,
S
,
μ
)
(X, \mathcal{S}, \mu)
(
X
,
S
,
μ
)
with
{
μ
(
E
)
:
E
∈
S
}
=
[
0
,
1
]
∪
[
3
,
c
]
.
\{\mu(E) : E \in \mathcal{S}\} = [0, 1] \cup [3, c].
{
μ
(
E
)
:
E
∈
S
}
=
[
0
,
1
]
∪
[
3
,
c
]
.
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