• 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

7.4. Lebesgue Integral

Example 7.4.2(c): Simple Functions

Recall the definition of the Dirichlet function:

In our new terminology, let Q be the set of all rational numbers. Then the Dirichlet function is simply the characteristic function of Q, i.e.

g(x) = X_Q(x)

Interactive Real Analysis, ver. 2.0.1(c)
(c) 1994-2018, Bert G. Wachsmuth
Page last modified: Jan 26, 2023