# Measure Measure lets you define *size* in any dimension. It is a general concept, of which *volume*, *area*, *length* and even *probability* are all special cases of it—in different dimensions or contexts. Formally, a measure is a function: $\mu: \text{subsets of space} \rightarrow [0, \infty]$ that satisfies three properties: 1. **Non-negativity**: $\mu(A) \geq 0$ 2. **Null empty set**: $\mu(\emptyset) = 0$ 3. **Countable additivity**: If $A_1, A_2, \dots$ are disjoint, then: $\mu\left(\bigcup_i A_i\right) = \sum_i \mu(A_i)$ --- Date: 20250723 Links to: Tags: References: * []()