Measure of the Cantor set plus the Cantor set

5,656

Here is the full question from Halmos's Problems for mathematicians, young and old: alt text

Here's the hint:

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And here's the solution:

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Updated on August 01, 2022

Comments

  • Admin
    Admin over 1 year

    The Sum of 2 sets of Measure zero might well be very large for example, the sum of $x$-axis and $y$-axis, is nothing but the whole plane. Similarly one can ask this question about Cantor sets:

    If $C$ is the cantor set, then what is the measure of $C+C$?

  • BlackJack
    BlackJack almost 13 years
    Were you ever a detective in a previous life? No $h*t. :)
  • Jonas Meyer
    Jonas Meyer almost 13 years
    @George S.: In this case, I just happen to be a Halmos fan who is also a fan of citing sources.