Measure

Last updated Nov 1, 2022

Let $X$ be a Nonempty Set and let $\mathcal{M}$ be a Sigma Algebra on $X$. Then $\mu: \mathcal{M} \to [0, \infty]$ is a Measure if

1. $\mu(\emptyset) = 0$
2. Countable Additivity of Measures: For any ${E_{n}}{n=1}^{\infty} \subset \mathcal{M}$, $\mu(\bigsqcup\limits{n \in \mathbb{N}} E_{n}) = \sum\limits_{n=1}^{\infty} \mu(E_{n})$.

• Extended Real Numbers
• Disjoint Sets