Question
5. By using properties of outer measure, prove that the interval [0, 1] is not countable.
5. By using properties of outer measure, prove that the interval [0, 1] is not countable.
Homework Answers
Answer #1
Let 
is
countable.
Then outer measure of is 
, because outer
measure of countable set is .
We also know that outer measure of 
is 
.
So 
This is contradiction our assumption so is
uncountable.
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