Interactive Real Analysis - part of MathCS.org

• Real Analysis
• 1. Sets and Relations
• 2. Infinity and Induction
• 3. Sequences of Numbers
• 4. Series of Numbers
• 5. Topology
• 6. Limits, Continuity, and Differentiation
• 7. The Integral
• 7.1. Riemann Integral
• 7.2. Integration Techniques
• 7.3. Measures
• 7.4. Lebesgue Integral
• 7.5. Riemann versus Lebesgue
• 8. Sequences of Functions
• 9. Historical Tidbits
• Java Tools

Example 7.3.1(g): Oddities of Riemann Integral

Why these ads ...

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

Back

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.