In mathematics, the Borel algebra is the smallest σalgebra on the real numbers R containing the intervals, and the Borel measure is the measure on this σalgebra which gives to the interval [a, b] the measure b − a (where a < b). Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...
In mathematics, the Borel algebra (or Borel Ïƒalgebra) on a topological space X is a Ïƒalgebra of subsets of X associated to the topology of X. In the mathematics literature, there are at least two inequivalent definitions of this Ïƒalgebra: The minimal Ïƒalgebra containing the open sets. ...
In mathematics, a σalgebra (or σfield) X over a set S is a family of subsets of S which is closed under countable set operations; σalgebras are mainly used in order to define measures on S. The concept is important in mathematical analysis and probability theory. ...
In mathematics, the real numbers are intuitively defined as numbers that are in onetoone correspondence with the points on an infinite lineâ€”the number line. ...
In mathematics, interval is a concept relating to the sequence and setmembership of one or more numbers. ...
In mathematics, a measure is a function that assigns a number, e. ...
The Borel measure is not complete, which is why in practice the complete Lebesgue measure is preferred: every Borel measurable set is also Lebesgue measurable, and the measures of the set agree. In measure theory, a complete measure is a measure in which every subset of every null set is measurable (having measure 0). ...
In mathematics, the Lebesgue measure is the standard way of assigning a volume to subsets of Euclidean space. ...
In a more general (abstract) measuretheoretic context, Let E be a Hausdorff space. A measure μ on the σalgebra (the Borel σalgebra on E) is Borel iff for all compact. In topology and related branches of mathematics, a Hausdorff space is a topological space in which points can be separated by neighbourhoods. ...
In mathematics, the Borel algebra (or Borel Ïƒalgebra) on a topological space X is a Ïƒalgebra of subsets of X associated to the topology of X. In the mathematics literature, there are at least two inequivalent definitions of this Ïƒalgebra: The minimal Ïƒalgebra containing the open sets. ...
