Induced measures on Wallman spaces

Yallaoui, El-Bachir

doi:10.1155/s0161171290001090

Cited by 3 publications

(3 citation statements)

References 6 publications

(4 reference statements)

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“…Some further related material can be found in [3,4,6,7,8,9]. We introduce the next results following Varadarajan who considered the lattice of zero sets in a Tychonoff space.…”

Section: Measure Terminologymentioning

confidence: 99%

On characterization and properties of replete Wallman spaces

Camacho

1995

Period Math Hung

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The subset of lattice regular zero~one valued measures on an algebra generated by a lattice (a Wallman-type space) which integrates all lattice continuous functions on an arbitrary set X is introduced and some properties of it are presented.Then repleteness of certain Waliman spaces is considered and used in finally establishing conditions whereby the space of lattice regular zero-one valued measures on the algebra generated by a lattice which are countably additive (a Wallman-type space) is realcompact.

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“…Some further related material can be found in [3,4,6,7,8,9]. We introduce the next results following Varadarajan who considered the lattice of zero sets in a Tychonoff space.…”

Section: Measure Terminologymentioning

confidence: 99%

On characterization and properties of replete Wallman spaces

Camacho

1995

Period Math Hung

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“…We give here a brief discussion of the general Wallman space (see also [11] [1]) yields for the conjugate space of Cb(_L ), namely Cb(_L )'= MR(_L where to any E C(_L )" there corresponds a unique u E MR(_L such that ,(f) f fdu, for all f C(L ). PROOF.…”

Section: The Wallman Space I(_l)mentioning

confidence: 99%

“…We next consider the space Q(L) of measures in t(L which integrate al___ [ [1,3,5,6,11]. However, the main definitions and notations used throughout the paper are presented for the reader's convenience in section 2(a).…”

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confidence: 99%

Realcompactification and repleteness of Wallman spaces

Camacho

1992

International Journal of Mathematics and Mathematical Sciences

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ABSTRACT. The extension of bounded lattice continuous functions on an arbitrary set x to the set of lattice regular zero-one measures on an algebra generated by a lattice (a Wallman-type space) is investigated.Next the subset of lattice regular zero-one measures on an algebra generated by a lattice which integrates all lattice continuous functions on X is introduced and various properties of it are presented.Finally conditions are established using repleteness criteria whereby the space of lattice regular zero-one measures on an algebra generated by a lattice which are countably additive (a Wallmantype space) is realcompact.

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