التحليل i need an example if any one know!!!

[Princess Moon]

السلام عليكم ورحمة الله وبركاته:
i need an example of a set A of positive outer measure but A contain no intevrals
to disprove this:
if A is a set of positive outer measure then the set A must contain an interval of positive length
وشكرا
^_^

 

[nanas]

You can take A as the complement of B (intersection of [0,1] and the set of rational numbers ) , where we note that B has outer measure zero , and hence Lebesgue measurable ... So its complement A also do , and has measure 1 .