7.3. Measures

Example 7.3.1(g): Oddities of Riemann Integral

There is a sequence of Riemann integrable functions fn that converges to another Riemann integrable function f but the corresponding sequence of Riemann integrals of fn does not converge to the integral of f.

We will talk about sequences of functions, convergence, and the like in the next chapter, but it seems desirable that if a sequnce of functions converges then the corresponding integrals should converge as well.

If you want to jump ahead to see an example of such a sequence, please click here.

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