STAT312 Lecture Notes - Infimum And Supremum

• School: University of Alberta
• Department: Statistics
• Course: STAT312
• Professor: Douglas Wiens

Document Summary

R; ber is the domain of function x. | (x) (a)| is continuous at a point a. Recall the de nition: the if, as (a) (equivalently, a, we have that (x) In mum and suprema (think min and max , but is a lower bound if. If there is a nite lower bound then there are many; the largest of them is the greatest lower bound ( Similarly with upper bound, least the inf is upper bound ( Here is a simple but very useful result (lab 5). and. If is continuous on a closed and bounded then it is bounded there. Thus the inf set and sup are nite, and are attained: there are points with for all (what can fail on an open domain?) If is continuous on a closed and bounded set then it is uniformly continuous there.