Mixing
Is the sum of two negligible sets always a negligible set?
0
$begingroup$
Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?
$E + F = {x + y : x ∈
E, y ∈ F}$
I tend to say no but I can't find any counter exemple
real-analysis measure-theory
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
$endgroup$
add a comment |
0
$begingroup$
Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?
$E + F = {x + y : x ∈
E, y ∈ F}$
I tend to say no but I can't find any counter exemple
real-analysis measure-theory
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
$endgroup$
add a comment |
0
0
0
$begingroup$
Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?
$E + F = {x + y : x ∈
E, y ∈ F}$
I tend to say no but I can't find any counter exemple
real-analysis measure-theory
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
$endgroup$
Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?
$E + F = {x + y : x ∈
E, y ∈ F}$
I tend to say no but I can't find any counter exemple
real-analysis measure-theory
real-analysis measure-theory
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
asked Jan 8 at 15:36
Jonathan BaramJonathan Baram
140113
140113
add a comment |
add a comment |
1 Answer
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In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
$endgroup$
2
$begingroup$
Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
$endgroup$
– Jonathan Baram
Jan 8 at 15:43
add a comment |
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1 Answer
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1 Answer
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active
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active
oldest
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active
oldest
votes
1
$begingroup$
In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
$endgroup$
2
$begingroup$
Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
$endgroup$
– Jonathan Baram
Jan 8 at 15:43
add a comment |
1
$begingroup$
In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
$endgroup$
2
$begingroup$
Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
$endgroup$
– Jonathan Baram
Jan 8 at 15:43
add a comment |
1
1
1
$begingroup$
In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
$endgroup$
In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
157k22126227
157k22126227
2
$begingroup$
Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
$endgroup$
– Jonathan Baram
Jan 8 at 15:43
add a comment |
2
$begingroup$
Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
$endgroup$
– Jonathan Baram
Jan 8 at 15:43
2
2
$begingroup$
Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
$endgroup$
– Jonathan Baram
Jan 8 at 15:43
$begingroup$
Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
$endgroup$
– Jonathan Baram
Jan 8 at 15:43
add a comment |
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