Borel Measure
In mathematics, specifically in measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let be the 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) < ∞ for every compact set 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, it is called a Radon measure. Note that a locally finite Borel measure automatically satisfies μ(C) < ∞ for every compact set C.
Read more about Borel Measure: On The Real Line
Famous quotes containing the word measure:
“As soon as man began considering himself the source of the highest meaning in the world and the measure of everything, the world began to lose its human dimension, and man began to lose control of it.”
—Václav Havel (b. 1936)