May be a simple question, but I still don't know what the definition of the supremum or infimum of a set in the extended real line is. For example when we define the Lebesgue measure, we define the Lebesgue outer measure as the infimum of a set in the extended real line. My questions are:
What is the definition of the supremum/infimum of a set in the extended real line?
FORMALLY, when do we say that the infimum of a set in the extended real line is equal to positive infinity?