specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors...

an outer measure μ on n-dimensional Euclidean space Rn is called a Borel regular measure if the following two conditions hold: Every Borel set B ⊆ Rn...

Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure. Borel sets and the associated Borel hierarchy also play a fundamental...

mathematician, he was known for his founding work in the areas of measure theory and probability. Borel was born in Saint-Affrique, Aveyron, the son of a Protestant...

other Borel sets is a Borel probability measure that is neither inner regular nor outer regular. Borel regular measure Radon measure Regularity theorem for...

mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological...

Lebesgue-measurable sets than there are Borel measurable sets. The Borel measure is translation-invariant, but not complete. The Haar measure can be defined on any locally...

theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco...

set that is not contained in the Borel sets. Hence, the Borel measure is not complete. n-dimensional Lebesgue measure is the completion of the n-fold product...

spectrum) of a measure μ {\displaystyle \mu } on a measurable topological space ( X , Borel ⁡ ( X ) ) {\displaystyle (X,\operatorname {Borel} (X))} is a...