Is $;F ={∅, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}$ a $;sigma$-algebra of $;{1, 2, 3}?$
0
$begingroup$
I think that it is not a $sigma$-algebra of ${1, 2, 3},$ because for example
${1, 2} cap {1, 3} = {1}$- ${1, 3} cap {2, 3} = {3}$
${1, 2}' = {3},$ etc.
which are not elements in $F.$ However, I'm not sure if this is right, because I'm not sure if I understand what a $sigma$-algebra is; I haven't heard it explained thoroughly.
probability-theory measure-theory
edited Jan 22 at 23:28
Henning Makholm
241k17308546
asked Jan 22 at 23:02
PEJPEJ
71
$endgroup$
add a comment |
0
$begingroup$
I think that it is not a $sigma$-algebra of ${1, 2, 3},$ because for example
${1, 2} cap {1, 3} = {1}$- ${1, 3} cap {2, 3} = {3}$
${1, 2}' = {3},$ etc.
which are not elements in $F.$ However, I'm not sure if this is right, because I'm not sure if I understand what a $sigma$-algebra is; I haven't heard it explained thoroughly.
probability-theory measure-theory
edited Jan 22 at 23:28
Henning Makholm
241k17308546
asked Jan 22 at 23:02
PEJPEJ
71
$endgroup$
2
$begingroup$
A $sigma$-algebra needs to be closed for finite intersections, so $F$ is not a $sigma$-algebra.
$endgroup$
– Laars Helenius
Jan 22 at 23:06
2
$begingroup$
@PEJ you understand it properly. Each of three examples that you give suffices to prove that it is not a sigma algebra.
$endgroup$
– user376343
Jan 22 at 23:14
$begingroup$
Alright, that's good to know. Thank you guys for your feedback.
$endgroup$
– PEJ
Jan 23 at 3:00
add a comment |
0
0
0
$begingroup$
I think that it is not a $sigma$-algebra of ${1, 2, 3},$ because for example
${1, 2} cap {1, 3} = {1}$- ${1, 3} cap {2, 3} = {3}$
${1, 2}' = {3},$ etc.
which are not elements in $F.$ However, I'm not sure if this is right, because I'm not sure if I understand what a $sigma$-algebra is; I haven't heard it explained thoroughly.
probability-theory measure-theory
edited Jan 22 at 23:28
Henning Makholm
241k17308546
asked Jan 22 at 23:02
PEJPEJ
71
$endgroup$
I think that it is not a $sigma$-algebra of ${1, 2, 3},$ because for example
${1, 2} cap {1, 3} = {1}$- ${1, 3} cap {2, 3} = {3}$
${1, 2}' = {3},$ etc.
which are not elements in $F.$ However, I'm not sure if this is right, because I'm not sure if I understand what a $sigma$-algebra is; I haven't heard it explained thoroughly.
probability-theory measure-theory
probability-theory measure-theory
edited Jan 22 at 23:28
Henning Makholm
241k17308546
asked Jan 22 at 23:02
PEJPEJ
71
edited Jan 22 at 23:28
Henning Makholm
241k17308546
asked Jan 22 at 23:02
PEJPEJ
71
edited Jan 22 at 23:28
Henning Makholm
241k17308546
edited Jan 22 at 23:28
Henning Makholm
241k17308546
edited Jan 22 at 23:28
Henning Makholm
241k17308546
241k17308546
asked Jan 22 at 23:02
PEJPEJ
71
asked Jan 22 at 23:02
PEJPEJ
71
asked Jan 22 at 23:02
PEJPEJ
71
71
2
$begingroup$
A $sigma$-algebra needs to be closed for finite intersections, so $F$ is not a $sigma$-algebra.
$endgroup$
– Laars Helenius
Jan 22 at 23:06
2
$begingroup$
@PEJ you understand it properly. Each of three examples that you give suffices to prove that it is not a sigma algebra.
$endgroup$
– user376343
Jan 22 at 23:14
$begingroup$
Alright, that's good to know. Thank you guys for your feedback.
$endgroup$
– PEJ
Jan 23 at 3:00
add a comment |
2
$begingroup$
A $sigma$-algebra needs to be closed for finite intersections, so $F$ is not a $sigma$-algebra.
$endgroup$
– Laars Helenius
Jan 22 at 23:06
2
$begingroup$
@PEJ you understand it properly. Each of three examples that you give suffices to prove that it is not a sigma algebra.
$endgroup$
– user376343
Jan 22 at 23:14
$begingroup$
Alright, that's good to know. Thank you guys for your feedback.
$endgroup$
– PEJ
Jan 23 at 3:00
2
2
$begingroup$
A $sigma$-algebra needs to be closed for finite intersections, so $F$ is not a $sigma$-algebra.
$endgroup$
– Laars Helenius
Jan 22 at 23:06
$begingroup$
A $sigma$-algebra needs to be closed for finite intersections, so $F$ is not a $sigma$-algebra.
$endgroup$
– Laars Helenius
Jan 22 at 23:06
2
2
$begingroup$
@PEJ you understand it properly. Each of three examples that you give suffices to prove that it is not a sigma algebra.
$endgroup$
– user376343
Jan 22 at 23:14
$begingroup$
@PEJ you understand it properly. Each of three examples that you give suffices to prove that it is not a sigma algebra.
$endgroup$
– user376343
Jan 22 at 23:14
$begingroup$
Alright, that's good to know. Thank you guys for your feedback.
$endgroup$
– PEJ
Jan 23 at 3:00
$begingroup$
Alright, that's good to know. Thank you guys for your feedback.
$endgroup$
– PEJ
Jan 23 at 3:00
add a comment |
0
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2
$begingroup$
A $sigma$-algebra needs to be closed for finite intersections, so $F$ is not a $sigma$-algebra.
$endgroup$
– Laars Helenius
Jan 22 at 23:06
2
$begingroup$
@PEJ you understand it properly. Each of three examples that you give suffices to prove that it is not a sigma algebra.
$endgroup$
– user376343
Jan 22 at 23:14
$begingroup$
Alright, that's good to know. Thank you guys for your feedback.
$endgroup$
– PEJ
Jan 23 at 3:00