Mixing
Finding a sequence of sets whose limit is a given set
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Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?
real-analysis measure-theory elementary-set-theory
asked 10 hours ago
M. Rahmat
292211
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up vote
1
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Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?
real-analysis measure-theory elementary-set-theory
asked 10 hours ago
M. Rahmat
292211
2
Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago
$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?
real-analysis measure-theory elementary-set-theory
asked 10 hours ago
M. Rahmat
292211
Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?
real-analysis measure-theory elementary-set-theory
real-analysis measure-theory elementary-set-theory
asked 10 hours ago
M. Rahmat
292211
asked 10 hours ago
M. Rahmat
292211
asked 10 hours ago
M. Rahmat
292211
asked 10 hours ago
M. Rahmat
292211
asked 10 hours ago
M. Rahmat
292211
292211
2
Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago
$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago
add a comment |
2
Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago
$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago
2
2
Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago
Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago
$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago
$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago
add a comment |
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2
Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago
$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago