1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lebesque Measure

  1. Aug 15, 2009 #1
    Suppose that E has Lebesque measure 0. Prove that the set {x^2 : x€E} has Lebesque measure 0.

    Please help me. I have a problem which is unsolveable for me. Thanks!
     
  2. jcsd
  3. Aug 15, 2009 #2
    Do you know a "change of variables" formula that expresses the measure of the set {x^2 : x in E} as an integral on E ?
     
  4. Aug 15, 2009 #3
    Honestly i have no idea about "change of variables" formula.I try to prove with outer measure formula but i failed.In my method i have difficulties about whether x^2 is subset of E or not. I made cases for it and for x^2 subset of E i made it but i think they can be disjoint sets.That is my failure point because i have no idea about this case.
     
  5. Aug 15, 2009 #4
    change of variables ... you have a "nice" map [itex]\phi[/itex] that maps a set E onto a set F, and a function [itex]f[/itex] defined on F . How to relate integrals involving [tex]f[/itex] on F and [itex]f \circ \phi[/itex] on E ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Lebesque Measure
  1. On Measurability (Replies: 1)

  2. Measuring Vectors (Replies: 3)

Loading...