Econ 519: David Reiley
Due Monday, 14 August 2006
The "finite covering property" (Section 29.5) is the most subtle and difficult concept in this chapter. It's most useful for understanding vector spaces other than Rn, such as (infinite-dimensional) spaces of functions (one place we worry about such spaces is in probability theory, where we often want to talk about whether a sequence of functions converges, such as in the Central Limit Theorem). In function spaces, the appropriate norm may not be obvious, so we would like a definition of compactness that doesn't depend on the norm (as "closed and bounded" does). Understanding the "finite covering property" is not essential for your mastery of economics, but it would be useful if you can get familiar with it and use it for practice in understanding proofs. So, if you're struggling, do the last three problems last.