Search results
Results From The WOW.Com Content Network
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe" [1]) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair (,) is called a measurable space.
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
In mathematics, given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space. Conceptually, this is similar to defining the Cartesian product of sets and the product topology of two topological spaces, except that there can be many natural choices for the product measure.
μ (1) For a cardinal μ, this is the same cardinal in the next higher type. *104.03 μ (1) For a cardinal μ, this is the same cardinal in the next lower type. *105.03 + The disjoint union of two classes *110.01 + c: The sum of two cardinals *110.02 Crp Short for "correspondence". *110.02 ς (A Greek sigma used at the end of a word.)
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics , science , and engineering for representing complex concepts and properties in a concise ...
The claim is that the Borel algebra is G ω 1, where ω 1 is the first uncountable ordinal number. That is, the Borel algebra can be generated from the class of open sets by iterating the operation G ↦ G δ σ . {\displaystyle G\mapsto G_{\delta \sigma }.} to the first uncountable ordinal.
This notation has also been used for other variants of floor and ceiling functions. 4. Iverson bracket: if P is a predicate, [] may denote the Iverson bracket, that is the function that takes the value 1 for the values of the free variables in P for which P is true, and takes the value 0 otherwise.
In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = (). Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [1] and twistor theory, [2] where it appears in the context of 2-spinors.