<abstract xmlns="http://www.w3.org/1999/xhtml"><p> For an Abelian, Archimedean Dedekind complete lattice-ordered, weakly <italic>σ</italic>-distributive group <italic>G </italic>and an algebra Ƒ</p><p><italic></italic>of subsets of a set <italic>X, </italic>every positive measure <italic>μ</italic>: Ƒ→<italic>G </italic>has a unique countably additive (in order convergence) extension to <italic>σ</italic>-algebra generated by Ƒ.</p></abstract>

For an Abelian, Archimedean Dedekind complete lattice-ordered, weakly σ-distributive group G and an algebra Ƒof subsets of a set X, every positive measure μ: Ƒ→G has a unique countably additive (in order convergence) extension to σ-algebra generated by Ƒ.

A note on measure extension problem of ℓ-group-valued measures

Departemt of Mathematics The Univerisity of Iowa Iowa City, Iowa 52242 U.S.A.

Tatra Mountains Mathematical Publications

{"article-title":"A note on measure extension problem of ℓ-group-valued measures"}

For an Abelian, Archimedean Dedekind complete lattice-ordered, weakly σ-distributive group G and an algebra Ƒof subsets of a set X, every positive measure μ:...

A note on measure extension problem of ℓ-group-valued measures

Published Online: Nov 12, 2012

Page range: 187 - 189

DOI: https://doi.org/10.2478/v10127-009-0017-6

Keywords
extremely disconnected compact Hausdorff spaces, lattice-valued measures

This content is open access.

A note on measure extension problem of ℓ-group-valued measures

Published Online: Nov 12, 2012

Page range: 187 - 189

DOI: https://doi.org/10.2478/v10127-009-0017-6

Keywordsextremely disconnected compact Hausdorff spaces, lattice-valued measures

This content is open access.

Keywords
extremely disconnected compact Hausdorff spaces, lattice-valued measures