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