Two principles for extending probability measures

Ascherl, Albert; Lehn, Jürgen

doi:10.1007/bf01176900

Cited by 30 publications

(10 citation statements)

References 10 publications

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“…By a result of Los-Marczewski [7,Theorem 4] [1,Corollary 4], the same is true in case ß is an analytic subset of a Polish space, 2 is its Borel a-field and 2' is an arbitrary a-generated sub-a-field of 2. However, if 2 is "much larger" than 2' it may happen that u is monogenic even though /a|2' is complete (see [10] or [11]).…”

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confidence: 74%

On Monogenic Operators and Measures

Lipecki¹,

Plachky²

1981

Proceedings of the American Mathematical Society

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Abstract. The notion of a monogenic operator between linear lattices, generalizing that of a monogenic measure, is introduced and investigated. The decomposition of an operator into its monogenic and antimonogenic parts is established. Products of monogenic measures are also considered.Introduction. We introduce the notion of a monogenic operator between linear lattices, i.e. of an order bounded linear operator which is determined in some sense by its restriction to a given linear sublattice. We prove that monogenic operators form a band (Theorem 1). This yields the decomposition of an arbitrary operator into its monogenic and antimonogenic parts. In a special case where operators are identified with real-valued measures on a a-field we get a generalization of a result of Johnson [4]. We compare our decomposition with some classical decompositions in measure theory (Examples 1 and 2). We also consider (not necessarily direct) products of monogenic measures (Theorem 2 and Example 3). As far as the linear-lattice-theoretical terminology is concerned we mostiy follow Jameson's

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confidence: 74%

On Monogenic Operators and Measures

Lipecki¹,

Plachky²

1981

Proceedings of the American Mathematical Society

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“…In recent years quite a lot of generalizations of Theorem B, where the arithmetic means in (1) and (3) were replaced by "generalized means", have been published [8], [15], [16], [21], [22]. We shall use here a modified version of the main result in [12] to derive a fairly abstract version of Theorem A.…”

Section: Fef Fefyeymentioning

confidence: 97%

Minimax theorems with one-sided randomization

Kindler

1995

Acta Math Hung

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“…But, by a theorem of Bierlein (see [4] or [1]), one can always extend a measure so that all members of a given countable partition of a measurable set are in the domain of the extension.…”

Section: It Follows That If We Definementioning

confidence: 99%