Set of Measure zero

  • Thread starter arvindam
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  • #1
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Main Question or Discussion Point

A set E subset of real numbers has measure zero. Set A={x2 : x[tex]\in[/tex]E}. How to prove that set A has measure zero?
(E could be any unbounded subset of R)
 

Answers and Replies

  • #2
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I would approximate E by open intervals. That is: there exists open intervals [tex]]a_i,b_i[[/tex] such that

[tex]E\subseteq \bigcup]a_i,b_i[[/tex]

and such that

[tex]\sum{b_i-a_i}<\epsilon[/tex].

Now square the open intervals to obtain an approximation of A.
 
  • #3
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But intervals are not bounded. b2i-a2i does not have a bound when b--ai is bounded.
 
  • #4
lavinia
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But intervals are not bounded. b2i-a2i does not have a bound when b--ai is bounded.
it is easy for any bounded set of measure zero. Split your set up into countably many of these.
 

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