Riesz space

Riesz space

In mathematics a Riesz space, lattice-ordered vector space or vector lattice is an ordered vector space where the order structure is a lattice.

Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper "Sur la décomposition des opérations fonctionelles linéaires".

Riesz spaces are important in measure theory.

Examples

* The space of continuous real valued function on a set "X" with compact support with the partial order "f" ≤ "g" is a Riesz space.

Properties

* Riesz spaces are lattice ordered groups
* Every Riesz space is a distributive lattice

References

* Bourbaki, Nicolas; Elements of Mathematics: Integration. Chapters 1–6; ISBN 3-540-41129-1
* Riesz, Frigyes; Sur la décomposition des opérations fonctionelles linéaires , Atti congress. internaz. mathematici (Bologna, 1928) , 3 , Zanichelli (1930) pp. 143–148
*


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Riesz space — /rees/, Math. a topological space in which sets containing one point are closed. [after Frigyes Riesz (1880 1956), Hungarian mathematician] * * * …   Universalium

  • Riesz space — /rees/, Math. a topological space in which sets containing one point are closed. [after Frigyes Riesz (1880 1956), Hungarian mathematician] …   Useful english dictionary

  • Riesz-Raum — Ein Riesz Raum ist ein Vektorraum mit einer Verbandsstruktur, die so beschaffen ist, dass sich die lineare und die Verbandsstruktur vertragen. Im Jahr 1928 wurde dieser Raum von Frigyes Riesz definiert[1] und trägt deshalb heute seinen Namen.… …   Deutsch Wikipedia

  • Riesz's lemma — is an lemma in functional analysis. It specifies (often easy to check) conditions which guarantee that a subspace in a normed linear space is dense. The result Before stating the result, we fix some notation. Let X be a normed linear space with… …   Wikipedia

  • Riesz representation theorem — There are several well known theorems in functional analysis known as the Riesz representation theorem. They are named in honour of Frigyes Riesz. The Hilbert space representation theorem This theorem establishes an important connection between a …   Wikipedia

  • Riesz–Thorin theorem — In mathematics, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem is a result about interpolation of operators. It is named after Marcel Riesz and his student G. Olof… …   Wikipedia

  • Riesz–Fischer theorem — In mathematics, the Riesz–Fischer theorem in real analysis refers to a number of closely related results concerning the properties of the space L2 of square integrable functions. The theorem was proven independently in 1907 by Frigyes Riesz and… …   Wikipedia

  • Riesz sequence — In mathematics, a sequence of vectors ( x n ) in a Hilbert space ( H , lang; , rang;) is called a Riesz sequence if there exist constants 0 …   Wikipedia

  • Riesz transform — In the mathematical theory of harmonic analysis, the Riesz transforms are a family of generalizations of the Hilbert transform to Euclidean spaces of dimension d > 1. They are a type of singular integral operator, meaning that they are given by a …   Wikipedia

  • Riesz-Thorin theorem — In mathematics, the Riesz Thorin theorem, often referred to as the Riesz Thorin Interpolation Theorem or the Riesz Thorin Convexity Theorem is a result about interpolation of operators . This should not be confused with somewhat different… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”