Fdtxjr

Calculus II Professor will not accept my correct integral evaluation that uses a different method, should I bring this up further?

How do I hide Chekhov's Gun?

Why is "das Weib" grammatically neuter?

Russian cases: A few examples, I'm really confused

It's a yearly task, alright

Replacing Windows 7 security updates with anti-virus?

Sword in the Stone story where the sword was held in place by electromagnets

Am I not good enough for you?

How to answer questions about my characters?

How to deal with taxi scam when on vacation?

Instead of Universal Basic Income, why not Universal Basic NEEDS?

Does this AnyDice function accurately calculate the number of ogres you make unconcious with three 4th-level castings of Sleep?

Have researchers managed to "reverse time"? If so, what does that mean for physics?

How is the Swiss post e-voting system supposed to work, and how was it wrong?

The use of "touch" and "touch on" in context

Is it true that real estate prices mainly go up?

Rules about breaking the rules. How do I do it well?

RegionDifference for Cylinder and Cuboid

How do anti-virus programs start at Windows boot?

Good allowance savings plan?

Professor being mistaken for a grad student

Old race car problem/puzzle

I need to drive a 7/16" nut but am unsure how to use the socket I bought for my screwdriver

How could a scammer know the apps on my phone / iTunes account?

What are good intuition for understanding that the pre image of a mesurable function on an element of a borel set is mesurable

What is the intuition behind the Borel Cantelli Lemma?Prove that if E is a measurable set, then the set whose elements are the squares of elements in E is also measurableIs the pre-image (through a measurable function) of a Lebesgue-measurable set also measurable?Is it true or false that every Lebesgue measurable set of a finite measure is contained in a Borel set of the same measure?For a Borel function when does there exist a set of full measure with measurable image$f:mathbb Rlongrightarrow mathbb R$ is measurable $iff$ $f^-1(B)$ is measurable for all Borel set $B$Is the pre-image of a Borel set by a continuous function a Borel set? Is it an open set?Cantor set to show that the Borel measure is not completeA function is a Borel function if and only if for any c, the set $f^-1((c,infty))$ is a Borel set(T/F) If $mu$ is a Borel measure on $mathbbR$ and $A$ is a Borel set such that $mu(A cap K) = 0$ for all compact sets $K$, then $mu(A) = 0$.

0

$begingroup$

I'm not convinced by the proof I saw in the lecture.

The statement is the following :

If $f$ is measurable, and if $B$ is in the borel set, then $f^-1 (B) in $ the set of measurables.

Can you please give me some intuition about this lemma and abiut the proof? I think it would be better to prove it using definition of the set of measurables.

measure-theory lebesgue-measure outer-measure

share|cite|improve this question

asked Mar 11 at 9:26

Marine GalantinMarine Galantin

875319

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  This is a definition of measurability, (at least for Borel measures) (not a lemma), and as such, requires no proof.
  $endgroup$
  – uniquesolution
  Mar 11 at 9:42
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have another definition of measurability. I have this one : en.wikipedia.org/wiki/Measurable_function
  $endgroup$
  – Marine Galantin
  Mar 11 at 22:42
  

  
  
  
  

add a comment | 

0

$begingroup$

I'm not convinced by the proof I saw in the lecture.

The statement is the following :

If $f$ is measurable, and if $B$ is in the borel set, then $f^-1 (B) in $ the set of measurables.

Can you please give me some intuition about this lemma and abiut the proof? I think it would be better to prove it using definition of the set of measurables.

measure-theory lebesgue-measure outer-measure

share|cite|improve this question

asked Mar 11 at 9:26

Marine GalantinMarine Galantin

875319

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  This is a definition of measurability, (at least for Borel measures) (not a lemma), and as such, requires no proof.
  $endgroup$
  – uniquesolution
  Mar 11 at 9:42
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have another definition of measurability. I have this one : en.wikipedia.org/wiki/Measurable_function
  $endgroup$
  – Marine Galantin
  Mar 11 at 22:42
  

  
  
  
  

add a comment | 

$begingroup$

I'm not convinced by the proof I saw in the lecture.

The statement is the following :

If $f$ is measurable, and if $B$ is in the borel set, then $f^-1 (B) in $ the set of measurables.

Can you please give me some intuition about this lemma and abiut the proof? I think it would be better to prove it using definition of the set of measurables.

measure-theory lebesgue-measure outer-measure

share|cite|improve this question

asked Mar 11 at 9:26

Marine GalantinMarine Galantin

875319

$endgroup$

share|cite|improve this question

asked Mar 11 at 9:26

Marine GalantinMarine Galantin

875319

share|cite|improve this question

asked Mar 11 at 9:26

Marine GalantinMarine Galantin

875319

asked Mar 11 at 9:26

Marine GalantinMarine Galantin

875319

asked Mar 11 at 9:26

Marine GalantinMarine Galantin

875319