${p in [1, infty]: f in L^p}$ is an interval?
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I understood the proof but why does this imply that ${p in [1, infty]: f in L^p}$ is an interval?
real-analysis measure-theory
asked Nov 24 at 8:27
conrad
707
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up vote
0
down vote
favorite
I understood the proof but why does this imply that ${p in [1, infty]: f in L^p}$ is an interval?
real-analysis measure-theory
asked Nov 24 at 8:27
conrad
707
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I understood the proof but why does this imply that ${p in [1, infty]: f in L^p}$ is an interval?
real-analysis measure-theory
asked Nov 24 at 8:27
conrad
707
I understood the proof but why does this imply that ${p in [1, infty]: f in L^p}$ is an interval?
real-analysis measure-theory
real-analysis measure-theory
asked Nov 24 at 8:27
conrad
707
asked Nov 24 at 8:27
conrad
707
asked Nov 24 at 8:27
conrad
707
asked Nov 24 at 8:27
conrad
707
asked Nov 24 at 8:27
conrad
707
707
add a comment |
add a comment |
1 Answer
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The inequality implies that if $fin L^p$ and $fin L^q$ for $p<q$, then $fin L^r$ for all $p<r<q$. This implies that the set is an interval.
answered Nov 24 at 11:37
Seewoo Lee
6,066826
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
The inequality implies that if $fin L^p$ and $fin L^q$ for $p<q$, then $fin L^r$ for all $p<r<q$. This implies that the set is an interval.
answered Nov 24 at 11:37
Seewoo Lee
6,066826
add a comment |
up vote
2
down vote
The inequality implies that if $fin L^p$ and $fin L^q$ for $p<q$, then $fin L^r$ for all $p<r<q$. This implies that the set is an interval.
answered Nov 24 at 11:37
Seewoo Lee
6,066826
add a comment |
up vote
2
down vote
up vote
2
down vote
The inequality implies that if $fin L^p$ and $fin L^q$ for $p<q$, then $fin L^r$ for all $p<r<q$. This implies that the set is an interval.
answered Nov 24 at 11:37
Seewoo Lee
6,066826
The inequality implies that if $fin L^p$ and $fin L^q$ for $p<q$, then $fin L^r$ for all $p<r<q$. This implies that the set is an interval.
answered Nov 24 at 11:37
Seewoo Lee
6,066826
answered Nov 24 at 11:37
Seewoo Lee
6,066826
answered Nov 24 at 11:37
Seewoo Lee
6,066826
answered Nov 24 at 11:37
Seewoo Lee
6,066826
6,066826
add a comment |
add a comment |
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