Timeline for Is there a name for finite unions of intervals?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| May 31 at 13:38 | history | edited | Pietro Majer |
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| May 31 at 13:33 | answer | added | Pietro Majer | timeline score: 7 | |
| May 31 at 10:11 | answer | added | André Henriques | timeline score: 8 | |
| May 29 at 10:08 | answer | added | Willie Wong | timeline score: 5 | |
| May 29 at 7:56 | history | edited | Pietro Majer | CC BY-SA 4.0 |
added 241 characters in body; edited tags
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| May 29 at 3:45 | comment | added | LSpice | Re, ah, right, sorry, I haven't taught measure theory for a while and forgot that's what "simple function" meant. | |
| May 29 at 2:19 | comment | added | Pietro Majer | @Lspice not exactly: a set is a finite union of intervals iff its characteristic functionis a step function . With simple functions we would get all measurable sets.... | |
| May 28 at 21:35 | comment | added | LSpice | I'm almost positive it was a joke (although I don't get it), but, in case anyone is tempted to use it as a reference, I believe that such sets are not universally referred to as funtervals. \\ Re, at least using left-open intervals, isn't a simple set with this definition exactly a set whose characteristic function is a simple function? | |
| May 28 at 21:13 | answer | added | Daniele Tampieri | timeline score: 15 | |
| May 28 at 9:30 | comment | added | Calliope Ryan-Smith | Such sets are key to o-minimal structures, but are never given a name when studied. Perhaps one could be very cheeky and refer to such sets as o-minimal. | |
| May 28 at 9:13 | comment | added | Pietro Majer | Yes, I'm aware of pluri-intervals. "Simple sets" is indeed the nicer choice up to now, but the meaning of "simple functions" is to me a fact more contra than pro (one would like a set to be an X-set iff its characteristic function is an X-function) | |
| May 28 at 8:59 | comment | added | Daniele Tampieri | Pluri-interval is used in the (old, 1950 circa) Italian school of mathematics (Picone, Miranda, Caccioppoli, Fichera etc.) to denote cartesian product of intervals. By using analogy to simple functions in Lebesgue integration theory, why do not call unions of intervals "simple sets"? | |
| May 28 at 8:46 | comment | added | Mikhail Katz | These are universally referred to as funtervals. Have lots of fun! | |
| May 28 at 7:20 | history | edited | Pietro Majer | CC BY-SA 4.0 |
minor edit
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| May 28 at 7:16 | comment | added | Pietro Majer | Since a linear combination of characteristic functions of interval is called a step function, it would also be nice to call these sets "step sets" but maybe it sounds too bizarre | |
| May 27 at 20:42 | comment | added | fedja | There is no canonical name, but you can always call anything like that "a simple set" for the purposes of one particular exposition (at least, that is what I do in my measure theory courses). You may want to be a bit careful about whether you allow open, closed, or half-open intervals, etc, not to run into a conflict with your own definitions but otherwise, if used frequently and consistently, such terminology is easy to absorb and to follow. | |
| May 27 at 19:40 | comment | added | Nick S | Space with finitely many connected components? :) | |
| May 27 at 19:36 | comment | added | Christian Remling | The analog of "finite intervals" is common in some contexts, despite the illogic. For example, a "finite gap potential" is a certain potential whose spectrum has finitely many gaps (= intervals not in the spectrum). | |
| May 27 at 19:31 | history | asked | Pietro Majer | CC BY-SA 4.0 |