Show that a function is Lebesgue measurable
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I have a function $f : [0,1[ rightarrow [0,1[$ and I want to show that the function is measurable.
Generally, I show that for every $a in mathbb R$, $f^{-1}(]-infty ; a])$ is Borel measurable.
But here I don't know how to proceed since the function is only defined on $[0,1[$
real-analysis measure-theory
edited Nov 18 at 14:05
mathnoob
1,137116
asked Nov 18 at 14:01
Jonathan Baram
142113
add a comment |
up vote
0
down vote
favorite
I have a function $f : [0,1[ rightarrow [0,1[$ and I want to show that the function is measurable.
Generally, I show that for every $a in mathbb R$, $f^{-1}(]-infty ; a])$ is Borel measurable.
But here I don't know how to proceed since the function is only defined on $[0,1[$
real-analysis measure-theory
edited Nov 18 at 14:05
mathnoob
1,137116
asked Nov 18 at 14:01
Jonathan Baram
142113
Can we check if for every $a in [0,1[, f^{-1}(]-infty;a]) cap mathbb{R}$ is Borel measurable?
– mathnoob
Nov 18 at 14:08
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a function $f : [0,1[ rightarrow [0,1[$ and I want to show that the function is measurable.
Generally, I show that for every $a in mathbb R$, $f^{-1}(]-infty ; a])$ is Borel measurable.
But here I don't know how to proceed since the function is only defined on $[0,1[$
real-analysis measure-theory
edited Nov 18 at 14:05
mathnoob
1,137116
asked Nov 18 at 14:01
Jonathan Baram
142113
I have a function $f : [0,1[ rightarrow [0,1[$ and I want to show that the function is measurable.
Generally, I show that for every $a in mathbb R$, $f^{-1}(]-infty ; a])$ is Borel measurable.
But here I don't know how to proceed since the function is only defined on $[0,1[$
real-analysis measure-theory
real-analysis measure-theory
edited Nov 18 at 14:05
mathnoob
1,137116
asked Nov 18 at 14:01
Jonathan Baram
142113
edited Nov 18 at 14:05
mathnoob
1,137116
asked Nov 18 at 14:01
Jonathan Baram
142113
edited Nov 18 at 14:05
mathnoob
1,137116
edited Nov 18 at 14:05
mathnoob
1,137116
edited Nov 18 at 14:05
mathnoob
1,137116
1,137116
asked Nov 18 at 14:01
Jonathan Baram
142113
asked Nov 18 at 14:01
Jonathan Baram
142113
asked Nov 18 at 14:01
Jonathan Baram
142113
142113
Can we check if for every $a in [0,1[, f^{-1}(]-infty;a]) cap mathbb{R}$ is Borel measurable?
– mathnoob
Nov 18 at 14:08
add a comment |
Can we check if for every $a in [0,1[, f^{-1}(]-infty;a]) cap mathbb{R}$ is Borel measurable?
– mathnoob
Nov 18 at 14:08
Can we check if for every $a in [0,1[, f^{-1}(]-infty;a]) cap mathbb{R}$ is Borel measurable?
– mathnoob
Nov 18 at 14:08
Can we check if for every $a in [0,1[, f^{-1}(]-infty;a]) cap mathbb{R}$ is Borel measurable?
– mathnoob
Nov 18 at 14:08
add a comment |
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Can we check if for every $a in [0,1[, f^{-1}(]-infty;a]) cap mathbb{R}$ is Borel measurable?
– mathnoob
Nov 18 at 14:08