Timeline for Continuity on a measure one set versus measure one set of points of continuity
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| S Oct 27, 2013 at 22:14 | history | suggested | Daniel Roy | CC BY-SA 3.0 |
Added that "g" has to be measurable, which we never said, but we wanted. If g need not be measurable then the conditions on the space X become much weaker, on the other hand. Also, swapped order of the last two paragraphs and added necessary condition of completeness to the Kuratowski comment.
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| Oct 27, 2013 at 22:09 | review | Suggested edits | |||
| S Oct 27, 2013 at 22:14 | |||||
| Oct 27, 2013 at 21:40 | vote | accept | Nate Ackerman | ||
| Oct 27, 2013 at 17:05 | answer | added | François G. Dorais | timeline score: 10 | |
| Oct 27, 2013 at 15:12 | answer | added | Jason Rute | timeline score: 4 | |
| Oct 27, 2013 at 12:54 | answer | added | Gerald Edgar | timeline score: 2 | |
| Oct 27, 2013 at 12:48 | answer | added | Gerald Edgar | timeline score: 7 | |
| S Oct 27, 2013 at 8:33 | history | suggested | Daniel Roy | CC BY-SA 3.0 |
added polish suggestion by Jason Rute
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| Oct 27, 2013 at 8:24 | review | Suggested edits | |||
| S Oct 27, 2013 at 8:33 | |||||
| S Oct 27, 2013 at 2:01 | history | suggested | Jason Rute |
Added a descriptive set theory tag, since I think this the sort of question descriptive set theorists think about.
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| Oct 27, 2013 at 1:45 | review | Suggested edits | |||
| S Oct 27, 2013 at 2:01 | |||||
| Oct 27, 2013 at 1:44 | comment | added | Jason Rute | I see my solution/comment above was wrong even if $Y=[0,1]$ (even when the lim sup is not $\infty$). I still think the answer to your question is yes (when $X$ and $Y$ are Polish), but whatever the proof is, it is going to be technical I think. You should add that $X$ and $Y$ are Polish spaces (I assume this is what you meant---since you cited Kechris). I'll add a "descriptive set theory" tag---since in my mind descriptive set theory is anything technical involving Polish spaces. :) | |
| Oct 26, 2013 at 21:55 | comment | added | Nate Ackerman | Thanks. However we are not assuming that Y is the real numbers and so there is not necessarily a natural ordering. Also, even when Y is the real numbers I believe that for many points not in the measure one set the limit will not exists (i.e. will be $\infty$) | |
| Oct 26, 2013 at 20:40 | history | edited | Ricardo Andrade |
replaced deprecated tag 'topology'
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| Oct 26, 2013 at 19:28 | comment | added | Jason Rute | I think the answer is yes. For each point not in the measure one set, let its value be the lim sup of all the values in a ball around it (restricted to the measure one set) as the radius goes to zero. Then by the definition of continuity this should work. I'll try to think about the details and write an answer later if no one else does. | |
| S Oct 26, 2013 at 18:55 | history | suggested | Daniel Roy | CC BY-SA 3.0 |
Put a brief version of the question at the start so that people browsing in Questions can see it without clicking through.
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| Oct 26, 2013 at 18:32 | review | Suggested edits | |||
| S Oct 26, 2013 at 18:55 | |||||
| Oct 26, 2013 at 17:25 | history | edited | Nate Ackerman |
edited tags
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| Oct 26, 2013 at 17:17 | history | asked | Nate Ackerman | CC BY-SA 3.0 |