Measure Theory problem
I know that the cardinality of the power set of R is strictly greater than c, and that the cardinality of the Borel sigma algebra on R is equal to c.
I'm supposed to use this to show that there is a Lebesgue measurable subset of R that is not a Borel set.
I'm a bit confused, because it seems like to do this I would have to show that there are Lebesgue measurable sets that are not Borel sets anyway apart from the cardinality argument, since not every subset of R is Lebesgue measurable.
Any advice on this?
Thanks; that makes a lot of sense now!