 However, from the point of view of the Lebesgue measure, the set of rational numbers is of measure zero; thus, what really matters is what happens in the complement of this set, where the function is given as arctan "x".It follows that the essential supremum is /2 while the essential infimum is −/2.On the other hand, consider the function "f"("x") = "x"3 defined for all real "x".