Outer measure of countable set is 0 (zero)

STILL have doubt :- watch this for complete understanding    • Explanation of outer measure of an co...  


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Outer measure of countable set is 0
To prove this
You should know some concepts about
Length of open and bounded interval.:-    • Length of an  Interval II lebesgue me...  
Cover of an set:-    • Cover :- How union of open and bounde...  
Outer measure is always non negative for an Interval (greater then or equal to zero):-    • Outer measure for an Interval  is alw...  
One theorem is used as mentioned in video:-
Example on outer measure:-    • Example of Outer measure  
defiination(outer measure):-    • Definition of Outer measure II HINDI ...  

Example A countable set has outer measure zero. Indeed, let C be a countable set
enumerated as C = {ck}k 1. Let E 0. For each natural number k, define Ik = (ck -E/2k+I ck+
E/2k+t ). The countable collection of open intervals {Ik}11 ° 1 covers C. Therefore