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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