Hello guys,
I would like to ask following:
Special case of Vitali theorem says, that if is set, for which there holds
(where means Lebesgue measure),
and system of closed intervals covers in Vitali sense (i.e. ),
then:
a) For any given there exists finite amount of pairwise disjoint intervals , such that
b) There exists countable substystem of (intervals in are pairwise disjoint), such that
where means outer Lebesgue measure.
I want to ask if there's any easy way how to prove, that
a) => b) and b)=> a), or the proofs have to be done separately.
Thank you very much