Webproblem has a complete solution for any subspace (or, indeed, any closed convex set) Y. This problem is often considered in calculus or linear algebra where it is called \least-squares" approximation. A large part of the current course will be taken up with least-squares approximations, too. For now let’s simply note that the problem WebWith the possible exception of Rudin's , this may be the single most assigned text for the all-important graduate real analysis course. And frankly, I have no idea how anyone can learn real analysis from this thing. The one thing that strikes you most about it is that Royden seems to shunt the most results to the execises.

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