Example of measure for some algebra over $mathbb N$
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 at 3:38
Lisa
265
add a comment |
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 at 3:38
Lisa
265
add a comment |
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 at 3:38
Lisa
265
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 at 3:38
Lisa
265
asked Nov 26 at 3:38
Lisa
265
edited Dec 3 at 9:22
asked Nov 26 at 3:38
Lisa
265
asked Nov 26 at 3:38
Lisa
265
asked Nov 26 at 3:38
Lisa
265
265
add a comment |
add a comment |
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "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
});
}
});
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%2f3013793%2fexample-of-measure-for-some-algebra-over-mathbb-n%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
To learn more, see our tips on writing great answers.
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%2f3013793%2fexample-of-measure-for-some-algebra-over-mathbb-n%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
