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content/Lectures/Lecture 14.md
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@ -18,6 +18,7 @@ For $A_{n} \in M$ **pairwise disjoint**
Example $M = \wp(X)$ define measure: Example $M = \wp(X)$ define measure:
$\mu(A) = \begin{cases}\#A & \text{When}\ A\ \text{is finite}\\ \infty & \text{When}\ n\ \text{is infinite}\end{cases}$ $\mu(A) = \begin{cases}\#A & \text{When}\ A\ \text{is finite}\\ \infty & \text{When}\ n\ \text{is infinite}\end{cases}$
--- ---
# Simple Function # Simple Function
A **simple function** on $X$ is a function $s : X \to \mathbb{R}$ of the form $s = \Sigma_{i=1}^{n} a_{i} \times X_{a_{i}}$ for pairwise disjoint $A_{i} \subset X$ and distinct real numbers $a_{i}$ A **simple function** on $X$ is a function $s : X \to \mathbb{R}$ of the form $s = \Sigma_{i=1}^{n} a_{i} \times X_{a_{i}}$ for pairwise disjoint $A_{i} \subset X$ and distinct real numbers $a_{i}$