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...

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...

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

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...

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...

{\displaystyle (Y,T)} are Borel spaces, a measurable function f : ( X , Σ ) → ( Y , T ) {\displaystyle f:(X,\Sigma )\to (Y,T)} is also called a Borel function. Continuous...