Example of measure for some algebra over $mathbb N$
$begingroup$
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 '18 at 3:38
LisaLisa
255
$endgroup$
add a comment |
$begingroup$
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 '18 at 3:38
LisaLisa
255
$endgroup$
add a comment |
$begingroup$
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 '18 at 3:38
LisaLisa
255
$endgroup$
$mathcal F$ is a set of events ($sigma$-algebra). Can you give an example for some algebra $mathcal A$ over $mathbb N$ a non-zero finite additive measure $mu $
on this algebra, which has a countably additive extension to the $sigma$-algebra generated by this algebra,
moreover, when shifting any set $A ∈ mathcal F$ by an integer $n$, for the so obtained set $A + n$
was fulfilled: $A + n ∈ A$, $mu (A + n) = mu $(A)?
probability-theory measure-theory examples-counterexamples outer-measure
probability-theory measure-theory examples-counterexamples outer-measure
asked Nov 26 '18 at 3:38
LisaLisa
255
asked Nov 26 '18 at 3:38
LisaLisa
255
edited Dec 3 '18 at 9:22
Lisa
asked Nov 26 '18 at 3:38
LisaLisa
255
asked Nov 26 '18 at 3:38
LisaLisa
255
asked Nov 26 '18 at 3:38
LisaLisa
255
255
add a comment |
add a comment |
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