borel measure
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In mathematics, specifically in Measure (mathematics)|measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let \mathfrak{B}(X) be the Sigma-algebra#Generated .CF.83-algebra|smallest σ-algebra that contains the open sets of X; this is known as the σ-algebra of Borel sets. Any measure μ defined on the σ-algebra of Borel sets is called a Borel measure. Some authors require in addition that μ(C)&nbsp;<&nbsp;∞ for every compact set&nbsp;C. If a Borel measure μ is both inner regular and outer regular, it is called a regular Borel measure. If μ is both inner regular and Locally finite measure|locally finite, it is called a Radon measure. Note that a locally finite Borel measure automatically satisfies μ(C)&nbsp;<&nbsp;∞ for every compact set&nbsp;C.
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