Measure and Integration 3 - Outer Measure

In this lecture, we discuss outer measure of any subset of R and show that outer measure of a countable set is zero. We also prove that outer measure is translation invariant and sub additive.
0:00 : outer measure , Gemotrical meaning
4:24 : property 1 : outer measure is always non negative
6:13 : property 2 : outer measure for empty set.
10:21 : property 3 : outer measure for finite set
20:03 : Property 4 : outer measure for a countable set .
27:56 : property 5 : outer measure is translation invariant.
41:05 : property 6 : outer measure is monotonic
45:51 : Property 7 : outer measure is countable sub-additive

[mathematicia]

0:00 : outer measure, Gemotrical meaning
4:24 : property 1 : outer measure is always non negative
6:13 : property 2 : outer measure for empty set.
10:21 : property 3 : outer measure for finite set
20:03 : Property 4 : outer measure for a countable set .
27:56 : property 5 : outer measure is translation invariant.
41:05 : property 6 : outer measure is monotonic
45:51 : Property 7 : outer measure is countable sub-additive

A small payback contribution by mine side on your hard work, by providing time stamps

Waiting for next lecture series.

[ktayeb]

But the inf may be infite; so must distinguish 2 cases, when you proove the sub additivity