Interactive Real Analysis
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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
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7.4. Lebesgue Integral
Proposition 7.4.14: Bounded Measurable Functions are Integrable
If
f
is a bounded function defined on a measurable set
E
with finite measure. Then
f
is measurable if and only if
f
is Lebesgue integrable.
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