# bounded set

In a sense, a bounded set has finite measure. What is that sense? There are notions for the real number line, metric spaces, and topological spaces.

## 1. for metric spaces

- For a metric space \((M,d)\), a subset \(X\) is called
*bounded*if there exists \(r>0\) such that for all \(s,t\in X\), we have \(d(s,t) < r\)