Math Is Fun Forum

Azathoth

Guest

Some questions about nonmeasurable sets

Ok, so it's known that the Cartesian product of measurable sets is measurable, and the measure of the product is product of the measures (i.e. if A, B are measurable, then m(AxB)=m(A)m(B) for some given measure m, for example the Lebesque measure). Now, how can I show that:
a) the product of nonmeasurable sets is nonmeasurable (i assume, it's not)
b)the product of nonmeasurable set and a measurble set with non-zero measure is nonmeasurable

P.S.: any help will be appreciated:D