Answer to Question #170536 in Real Analysis for Prathibha Rose

Question

Let a,b,c,d element of R with a<b &c<d then show that every real valued convex function on the closed rectangle [a,b]×[c,d] in R² is bounded

Answer 1

The region [a,b] × [c,d] is a closed rectangle. And a closed rectangle is both a closed and a bounded set. Also, we have that a convex function defined on a closed set yields a closed function. This information provides us the conclusion to say f is continuous and hence bounded