The cardinality of Lebesgue sets Suppose $A=\{S\;|\;S \subset \mathbb R^n, S\text{ is Lebesgue measurable}\}$. What is the cardinality of $A$? Is it the same as the cardinality of all of the real numbers?

Hint:
Note that the Cantor set, or some copy of it in $\Bbb R^n$ is Lebesgue measurable with measure zero.


*

*Every subset of a null set is measurable.

*The cardinality of the Cantor set is $2^{\aleph_0}$.

