Nonmeasurable functions
and paradoxical decompositions

 

 

I used this handout in a first year graduate course in real variables. The idea was to to do a little more with nonmeasurable sets than we found in our textbook. The notes end up interpreting the usual construction of a nonmeasurable set as providing a "paradoxical decomposition" of the unit circle. This gives an excuse to say a few words (no proofs) about the Banach-Tarski paradox.

 

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