Convergence in L1 implies convergence of Integrals

Last updated Nov 1, 2022

TODO

• L1 Integrable Functions
• Sequence Convergence
• Integration

If $f_{n} \overset{L^{1}}{\to} f$, then $\int\limits f_{n} \to \int\limits f$. This follows because

$$\int\limits |f_{n} - f| \geq \left| \int\limits f_{n} -f \right| = \left| \int\limits f_{n} - \int\limits f \right| \geq 0$$