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
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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
1,10511
add a comment |
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1 Answer
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1 Answer
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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
1,10511
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
1,10511
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
1,10511
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
1,10511
answered Nov 26 at 14:58
Sorin Tirc
1,10511
answered Nov 26 at 14:58
Sorin Tirc
1,10511
answered Nov 26 at 14:58
Sorin Tirc
1,10511
1,10511
add a comment |
add a comment |
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