Riesz space

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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.

[edit] 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.

[edit] Properties

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

[edit] References

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