# The measure extension problem for vector lattices

Annales de l'institut Fourier (1971)

- Volume: 21, Issue: 4, page 65-85
- ISSN: 0373-0956

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topWright, J. D. Maitland. "The measure extension problem for vector lattices." Annales de l'institut Fourier 21.4 (1971): 65-85. <http://eudml.org/doc/74062>.

@article{Wright1971,

abstract = {Let $V$ be a boundedly $\sigma $-complete vector lattice. If each $V$-valued premeasure on an arbitrary field of subsets of an arbitrary set can be extended to a $\sigma $-additive measure on the generated $\sigma $-field then $V$ is said to have the measure extension property. Various sufficient conditions on $V$ which ensure that it has this property are known. But a complete characterisation of the property, that is, necessary and sufficient conditions, is obtained here. One of the most useful characterisations is: $V$has the measure extension property if, and only if, each $V$-valued Baire measure on each compact Hausdorff space is regular. This leads to an intrinsic algebraic characterisation: $V$has the measure extension property if, and only if, $V$ is weakly $\sigma $-distributive.},

author = {Wright, J. D. Maitland},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {4},

pages = {65-85},

publisher = {Association des Annales de l'Institut Fourier},

title = {The measure extension problem for vector lattices},

url = {http://eudml.org/doc/74062},

volume = {21},

year = {1971},

}

TY - JOUR

AU - Wright, J. D. Maitland

TI - The measure extension problem for vector lattices

JO - Annales de l'institut Fourier

PY - 1971

PB - Association des Annales de l'Institut Fourier

VL - 21

IS - 4

SP - 65

EP - 85

AB - Let $V$ be a boundedly $\sigma $-complete vector lattice. If each $V$-valued premeasure on an arbitrary field of subsets of an arbitrary set can be extended to a $\sigma $-additive measure on the generated $\sigma $-field then $V$ is said to have the measure extension property. Various sufficient conditions on $V$ which ensure that it has this property are known. But a complete characterisation of the property, that is, necessary and sufficient conditions, is obtained here. One of the most useful characterisations is: $V$has the measure extension property if, and only if, each $V$-valued Baire measure on each compact Hausdorff space is regular. This leads to an intrinsic algebraic characterisation: $V$has the measure extension property if, and only if, $V$ is weakly $\sigma $-distributive.

LA - eng

UR - http://eudml.org/doc/74062

ER -

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- [12] R. SIKORSKI, Boolean algebras, Springer (1962) (Second edition).
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- [15] J. D. MAITLAND WRIGHT, "Stone-algebra-valued measures and integrals", Proc. London Math. Soc., (3), 19, 107-122 (1969). Zbl0186.46504MR39 #1625
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