lemmas about Lebesgue's outer measure #1293
Merged
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Motivation for this change
Four lemmas about the Lebesgue measure.
The second one is actually the most interesting because we use to prove
an important corollary of the Vitali's theorem (PR to come)
outer_measure_open_itv_cover
:definition of the outer measure in terms of covers of open intervals
(proposition 20 in Li)
outer_measure_open
:for a set A with bounded outer measure and an epsilon,
there is an open that contains A and whose measure is
less than the outer measure A + epsilon,
(proposition 21 1) in Li)
outer_measure_Gdelta
:for a set A with bounded outer measure, there exists a G-delta sets
that contains A and whose measure is the same as A
(proposition 21 2) in Li)
negligible_outer_measure
:a set N is negligible for the lebesgue measure iff its outer measure is 0
(corollary 22 in Li)
Checklist
CHANGELOG_UNRELEASED.md
Reference: How to document
Reminder to reviewers