Every locally finite measure space is regular
Prove that every locally finite measure space is regular.
I am not sure how to go about this problem. Certainly, this can be shown to be true for any ball of finite measure that is contained in a larger ball by local finiteness and continuity of finite measure from above and below, but how would I go about proving this for an arbitrary set $A$?
measure-theory
edited Nov 26 at 11:40
John Hughes
62.3k24090
asked Nov 26 at 10:31
Cute Brownie
995416
add a comment |
Prove that every locally finite measure space is regular.
I am not sure how to go about this problem. Certainly, this can be shown to be true for any ball of finite measure that is contained in a larger ball by local finiteness and continuity of finite measure from above and below, but how would I go about proving this for an arbitrary set $A$?
measure-theory
edited Nov 26 at 11:40
John Hughes
62.3k24090
asked Nov 26 at 10:31
Cute Brownie
995416
add a comment |
Prove that every locally finite measure space is regular.
I am not sure how to go about this problem. Certainly, this can be shown to be true for any ball of finite measure that is contained in a larger ball by local finiteness and continuity of finite measure from above and below, but how would I go about proving this for an arbitrary set $A$?
measure-theory
edited Nov 26 at 11:40
John Hughes
62.3k24090
asked Nov 26 at 10:31
Cute Brownie
995416
Prove that every locally finite measure space is regular.
I am not sure how to go about this problem. Certainly, this can be shown to be true for any ball of finite measure that is contained in a larger ball by local finiteness and continuity of finite measure from above and below, but how would I go about proving this for an arbitrary set $A$?
measure-theory
measure-theory
edited Nov 26 at 11:40
John Hughes
62.3k24090
asked Nov 26 at 10:31
Cute Brownie
995416
edited Nov 26 at 11:40
John Hughes
62.3k24090
asked Nov 26 at 10:31
Cute Brownie
995416
edited Nov 26 at 11:40
John Hughes
62.3k24090
edited Nov 26 at 11:40
John Hughes
62.3k24090
edited Nov 26 at 11:40
John Hughes
62.3k24090
62.3k24090
asked Nov 26 at 10:31
Cute Brownie
995416
asked Nov 26 at 10:31
Cute Brownie
995416
asked Nov 26 at 10:31
Cute Brownie
995416
995416
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
I don't know where you got this problem from, but it seems to be false, see for example the third example from this section:
https://en.wikipedia.org/wiki/Regular_measure#Inner_regular_measures_that_are_not_outer_regular
You have a locally finite measure there that is inner-regular but not outer-regular(and hence not regular).
answered Nov 26 at 14:58
Sorin Tirc
1,370113
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
});
}
});
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%2f3014163%2fevery-locally-finite-measure-space-is-regular%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
I don't know where you got this problem from, but it seems to be false, see for example the third example from this section:
https://en.wikipedia.org/wiki/Regular_measure#Inner_regular_measures_that_are_not_outer_regular
You have a locally finite measure there that is inner-regular but not outer-regular(and hence not regular).
answered Nov 26 at 14:58
Sorin Tirc
1,370113
add a comment |
I don't know where you got this problem from, but it seems to be false, see for example the third example from this section:
https://en.wikipedia.org/wiki/Regular_measure#Inner_regular_measures_that_are_not_outer_regular
You have a locally finite measure there that is inner-regular but not outer-regular(and hence not regular).
answered Nov 26 at 14:58
Sorin Tirc
1,370113
add a comment |
I don't know where you got this problem from, but it seems to be false, see for example the third example from this section:
https://en.wikipedia.org/wiki/Regular_measure#Inner_regular_measures_that_are_not_outer_regular
You have a locally finite measure there that is inner-regular but not outer-regular(and hence not regular).
answered Nov 26 at 14:58
Sorin Tirc
1,370113
I don't know where you got this problem from, but it seems to be false, see for example the third example from this section:
https://en.wikipedia.org/wiki/Regular_measure#Inner_regular_measures_that_are_not_outer_regular
You have a locally finite measure there that is inner-regular but not outer-regular(and hence not regular).
answered Nov 26 at 14:58
Sorin Tirc
1,370113
answered Nov 26 at 14:58
Sorin Tirc
1,370113
answered Nov 26 at 14:58
Sorin Tirc
1,370113
answered Nov 26 at 14:58
Sorin Tirc
1,370113
1,370113
add a comment |
add a comment |
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%2f3014163%2fevery-locally-finite-measure-space-is-regular%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
