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. ),
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