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
1
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
156k22126227
$endgroup$
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 |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3066317%2fis-the-sum-of-two-negligible-sets-always-a-negligible-set%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
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
156k22126227
$endgroup$
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
156k22126227
$endgroup$
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
156k22126227
$endgroup$
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
156k22126227
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
156k22126227
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
156k22126227
answered Jan 8 at 15:39
José Carlos SantosJosé Carlos Santos
156k22126227
156k22126227
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 |
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3066317%2fis-the-sum-of-two-negligible-sets-always-a-negligible-set%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
