Measure Extensions by Conditional Atoms.
Wolfgang Hackenbroch (1988/89)
Mathematische Zeitschrift
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Wolfgang Hackenbroch (1988/89)
Mathematische Zeitschrift
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Monika Remy (1988)
Manuscripta mathematica
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Manfred Droste (1984)
Manuscripta mathematica
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Hans-Berndt Brinkmann (1969)
Manuscripta mathematica
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Otto Endler (1975)
Manuscripta mathematica
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J. Łoś, Edward Marczewski (1949)
Fundamenta Mathematicae
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Heinz König (1985)
Mathematische Zeitschrift
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Baltasar Rodríguez-Salinas (2001)
RACSAM
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We give necessary and sufficient conditions for a totally ordered by extension family (Ω, Σ, μ) of spaces of probability to have a measure μ which is an extension of all the measures μ. As an application we study when a probability measure on Ω has an extension defined on all the subsets of Ω.
Werner Rinkewitz (2001)
Colloquium Mathematicae
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Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.
Jürgen Lehn, Albert Ascherl (1977)
Manuscripta mathematica
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Anna De Simone, Pavel Pták (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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In [4] it is proved that a measure on a finite coarse-grained space extends, as a signed measure, over the entire power algebra. In [7] this result is reproved and further improved. Both the articles [4] and [7] use the proof techniques of linear spaces (i.e. they use multiplication by real scalars). In this note we show that all the results cited above can be relatively easily obtained by the Horn-Tarski extension technique in a purely combinatorial manner. We also characterize the...
B. Jessen (1948)
Colloquium Mathematicae
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Michael Langenbruch (1994)
Manuscripta mathematica
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Ricardo Faro Rivas, Juan A. Navarro, Juan Sancho (1994)
Extracta Mathematicae
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