Definition:Borel Measure

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Definition

Let $\struct {X, \tau}$ be a topological space.

Let $\map \BB {X, \tau}$ be the Borel $\sigma$-algebra on $\struct {X, \tau}$.

Let $\mu$ be a measure on $\map \BB {X, \tau}$ such that:

$\map \mu K < \infty$ for all compact $K \subseteq X$.

We say that $\mu$ is a Borel measure.

Also see

• Definition:Signed Borel Measure
• Definition:Radon Measure

• Results about Borel measures can be found here.

Source of Name

This entry was named for Émile Borel.

Sources

• 2014: Gerald Teschl: Mathematical Methods in Quantum Mechanics With Applications to Schrödinger Operators (2nd ed.) ... (previous) ... (next): $\text A.1$: Borel measures in a nutshell