Why are open sets denoted $U$, $G$, and measurable sets $E$?
$begingroup$
Why are open sets usually denoted by $U$?
Is there a reference about this?
Sometimes open set uses the letter $G$, such as $G_{delta} $ set.
I also wonder the meaning of $G$.
Additional question: Why do we use or who first used $E$ to denote a subset in measure theory?
general-topology measure-theory notation math-history
edited Dec 7 '18 at 16:06
rfabbri
1728
asked Dec 6 '18 at 8:14
user365200user365200
454
$endgroup$
add a comment |
$begingroup$
Why are open sets usually denoted by $U$?
Is there a reference about this?
Sometimes open set uses the letter $G$, such as $G_{delta} $ set.
I also wonder the meaning of $G$.
Additional question: Why do we use or who first used $E$ to denote a subset in measure theory?
general-topology measure-theory notation math-history
edited Dec 7 '18 at 16:06
rfabbri
1728
asked Dec 6 '18 at 8:14
user365200user365200
454
$endgroup$
$begingroup$
This is a very good question. My naive guess would be because $U$ will always be the union of basic open sets (e.g. open balls)...
$endgroup$
– Ivo Terek
Dec 6 '18 at 8:50
$begingroup$
And why $F$ is always used to denote closed sets?
$endgroup$
– Thomas Shelby
Dec 6 '18 at 8:54
2
$begingroup$
Possible duplicate of math.stackexchange.com/questions/520290/…
$endgroup$
– lhf
Dec 6 '18 at 9:56
add a comment |
$begingroup$
Why are open sets usually denoted by $U$?
Is there a reference about this?
Sometimes open set uses the letter $G$, such as $G_{delta} $ set.
I also wonder the meaning of $G$.
Additional question: Why do we use or who first used $E$ to denote a subset in measure theory?
general-topology measure-theory notation math-history
edited Dec 7 '18 at 16:06
rfabbri
1728
asked Dec 6 '18 at 8:14
user365200user365200
454
$endgroup$
Why are open sets usually denoted by $U$?
Is there a reference about this?
Sometimes open set uses the letter $G$, such as $G_{delta} $ set.
I also wonder the meaning of $G$.
Additional question: Why do we use or who first used $E$ to denote a subset in measure theory?
general-topology measure-theory notation math-history
general-topology measure-theory notation math-history
edited Dec 7 '18 at 16:06
rfabbri
1728
asked Dec 6 '18 at 8:14
user365200user365200
454
edited Dec 7 '18 at 16:06
rfabbri
1728
asked Dec 6 '18 at 8:14
user365200user365200
454
edited Dec 7 '18 at 16:06
rfabbri
1728
edited Dec 7 '18 at 16:06
rfabbri
1728
edited Dec 7 '18 at 16:06
rfabbri
1728
1728
asked Dec 6 '18 at 8:14
user365200user365200
454
asked Dec 6 '18 at 8:14
user365200user365200
454
asked Dec 6 '18 at 8:14
user365200user365200
454
454
$begingroup$
This is a very good question. My naive guess would be because $U$ will always be the union of basic open sets (e.g. open balls)...
$endgroup$
– Ivo Terek
Dec 6 '18 at 8:50
$begingroup$
And why $F$ is always used to denote closed sets?
$endgroup$
– Thomas Shelby
Dec 6 '18 at 8:54
2
$begingroup$
Possible duplicate of math.stackexchange.com/questions/520290/…
$endgroup$
– lhf
Dec 6 '18 at 9:56
add a comment |
$begingroup$
This is a very good question. My naive guess would be because $U$ will always be the union of basic open sets (e.g. open balls)...
$endgroup$
– Ivo Terek
Dec 6 '18 at 8:50
$begingroup$
And why $F$ is always used to denote closed sets?
$endgroup$
– Thomas Shelby
Dec 6 '18 at 8:54
2
$begingroup$
Possible duplicate of math.stackexchange.com/questions/520290/…
$endgroup$
– lhf
Dec 6 '18 at 9:56
$begingroup$
This is a very good question. My naive guess would be because $U$ will always be the union of basic open sets (e.g. open balls)...
$endgroup$
– Ivo Terek
Dec 6 '18 at 8:50
$begingroup$
This is a very good question. My naive guess would be because $U$ will always be the union of basic open sets (e.g. open balls)...
$endgroup$
– Ivo Terek
Dec 6 '18 at 8:50
$begingroup$
And why $F$ is always used to denote closed sets?
$endgroup$
– Thomas Shelby
Dec 6 '18 at 8:54
$begingroup$
And why $F$ is always used to denote closed sets?
$endgroup$
– Thomas Shelby
Dec 6 '18 at 8:54
2
2
$begingroup$
Possible duplicate of math.stackexchange.com/questions/520290/…
$endgroup$
– lhf
Dec 6 '18 at 9:56
$begingroup$
Possible duplicate of math.stackexchange.com/questions/520290/…
$endgroup$
– lhf
Dec 6 '18 at 9:56
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
For $G_delta$ set and $F_sigma$ set, each of this is from german word Gebiet and french word fermé respectively.
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
$endgroup$
add a comment |
$begingroup$
$U$ stands for Umgebung. Reference: https://de.m.wikipedia.org/wiki/Umgebung_(Mathematik) This is the German wikipedia article corresponding to Neighborhood.
More complete history on this in Why do we traditionally use letter U for open sets?
$E$ stands for Ensemble, which is French for set. You can see it used in Lebesgue’s original paper to denote arbitrary measurable sets, so that it became tradition https://fermatslibrary.com/s/on-a-generalization-of-the-definite-integral
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
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oldest
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$begingroup$
For $G_delta$ set and $F_sigma$ set, each of this is from german word Gebiet and french word fermé respectively.
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
$endgroup$
add a comment |
$begingroup$
For $G_delta$ set and $F_sigma$ set, each of this is from german word Gebiet and french word fermé respectively.
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
$endgroup$
add a comment |
$begingroup$
For $G_delta$ set and $F_sigma$ set, each of this is from german word Gebiet and french word fermé respectively.
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
$endgroup$
For $G_delta$ set and $F_sigma$ set, each of this is from german word Gebiet and french word fermé respectively.
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
answered Dec 6 '18 at 9:01
Lee.HWLee.HW
1137
1137
add a comment |
add a comment |
$begingroup$
$U$ stands for Umgebung. Reference: https://de.m.wikipedia.org/wiki/Umgebung_(Mathematik) This is the German wikipedia article corresponding to Neighborhood.
More complete history on this in Why do we traditionally use letter U for open sets?
$E$ stands for Ensemble, which is French for set. You can see it used in Lebesgue’s original paper to denote arbitrary measurable sets, so that it became tradition https://fermatslibrary.com/s/on-a-generalization-of-the-definite-integral
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
$endgroup$
add a comment |
$begingroup$
$U$ stands for Umgebung. Reference: https://de.m.wikipedia.org/wiki/Umgebung_(Mathematik) This is the German wikipedia article corresponding to Neighborhood.
More complete history on this in Why do we traditionally use letter U for open sets?
$E$ stands for Ensemble, which is French for set. You can see it used in Lebesgue’s original paper to denote arbitrary measurable sets, so that it became tradition https://fermatslibrary.com/s/on-a-generalization-of-the-definite-integral
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
$endgroup$
add a comment |
$begingroup$
$U$ stands for Umgebung. Reference: https://de.m.wikipedia.org/wiki/Umgebung_(Mathematik) This is the German wikipedia article corresponding to Neighborhood.
More complete history on this in Why do we traditionally use letter U for open sets?
$E$ stands for Ensemble, which is French for set. You can see it used in Lebesgue’s original paper to denote arbitrary measurable sets, so that it became tradition https://fermatslibrary.com/s/on-a-generalization-of-the-definite-integral
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
$endgroup$
$U$ stands for Umgebung. Reference: https://de.m.wikipedia.org/wiki/Umgebung_(Mathematik) This is the German wikipedia article corresponding to Neighborhood.
More complete history on this in Why do we traditionally use letter U for open sets?
$E$ stands for Ensemble, which is French for set. You can see it used in Lebesgue’s original paper to denote arbitrary measurable sets, so that it became tradition https://fermatslibrary.com/s/on-a-generalization-of-the-definite-integral
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
edited Dec 7 '18 at 15:35
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
answered Dec 6 '18 at 9:34
rfabbrirfabbri
1728
1728
add a comment |
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$begingroup$
This is a very good question. My naive guess would be because $U$ will always be the union of basic open sets (e.g. open balls)...
$endgroup$
– Ivo Terek
Dec 6 '18 at 8:50
$begingroup$
And why $F$ is always used to denote closed sets?
$endgroup$
– Thomas Shelby
Dec 6 '18 at 8:54
2
$begingroup$
Possible duplicate of math.stackexchange.com/questions/520290/…
$endgroup$
– lhf
Dec 6 '18 at 9:56