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quiz4

# quiz4 - 2 Is it true that f A ⊂ R n → R is integrable...

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Spring 2006 Math 332 - Real Analysis II Quiz 4, 17/5/2006 1. Is there a relation between countability and being measure zero in R n ? That is, which of the following is true/false? Why? (a) A measure zero set is necessarily countable. (b) A measure zero set is necessarily uncountable. (c) A countable set has necessarily measure zero. (d) An uncountable set has necessarily measure zero.
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Unformatted text preview: 2. Is it true that f : A ⊂ R n → R is integrable whenever (a) A has measure zero? If yes, prove; if no, give a counterexample. (b) A has volume zero? If yes, prove; if no, give a counterexample and then impose the least restrictive condition on f to guarantee its integrability. Ferit ¨ Ozt¨urk, Bo˘gazi¸ci University 2006...
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