Borel Set

From: Man (sudjok_at_yahoo.com)
Date: 09/29/04 

Date: Wed, 29 Sep 2004 12:42:09 +0000 (UTC)

Prove that a Borel set B in B^d is an L-B-null set if and only if one of
the two following conditions is satisfied:
(a) For every eps>0 there is a covering of B by countably many open

intervals I_n in R^d such that sum_n=1^infty{m^d(I_n)}<eps.

(b)There is a covering of B by countably many open intervals I_n such that
sum_n=1^infty{m^d(I_n)}<+infty and every point of B lies in I_n for

infinitely many n.

Both characterizations remain valid if the I_n are allowed to be half-open
or compact, instead of open.

m^d - Lebesgue-Borel measure (L-B measure) on R^d.

Thanks for your help.