Chapter 5

5.2. Uniform convergence 59 Example 5.7. Define fn: R → R by fn(x) = (1+ x n)n. Then by the limit formula for the exponential, which we do not prove here, fn → ex pointwise on R. 5.2. Uniform convergence In this section, we introduce a stronger notion of convergence of functions than pointwise convergence, called uniform convergence. The ...

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