Almost strong liftings and τ-additivity

Babiker, Abdel; Strauss, W.

doi:10.1007/bfb0088225

Cited by 8 publications

(10 citation statements)

References 8 publications

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“…we denote by A (/A) the system of all liftings. For any p e A(/z) there exists exactly one (multiplicative) lifting p (in the sense of [16, Chapter III, Section 1, Definition 2]) on Jzf°°(/z), the space of all bounded E-measurable functions on Q, such that P(XA) = X P (A) for all A e E (\A denotes the characteristic function of [3] On products of almost strong liftings 313…”

Section: Preliminariesmentioning

confidence: 99%

On products of almost strong liftings

Macheras

Strauss

1996

J Aust Math Soc A

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Dealing with a problem posed by Kupka we give results concerning the permanence of the almost strong lifting property (respectively of the universal strong lifting property) under finite and countable products of topological probability spaces. As a basis we prove a theorem on the existence of liftings compatible with products for general probability spaces, and in addition we use this theorem for discussing finite products of lifting topologies.

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Section: Preliminariesmentioning

confidence: 99%

On products of almost strong liftings

Macheras

Strauss

1996

J Aust Math Soc A

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“…From this, one easily concludes that for a general metric space T, strong lifting compactness is equivalent to measure compactness, and this in turn is equivalent to the condition that every closed discrete subspace of T have non-measurable cardinal. Clearly this is not true in general, since measure compactness does not even imply lifting compactness, a condition which lies strictly between strong measure compactness and measure compactness (see A. Bellow [2]). V. Losert's counterexample in [11] together with 2.3 shows that neither lifting compactness nor strong measure compactness imply strong lifting compactness.…”

Section: Strongly Lifting Compact Spacesmentioning

confidence: 99%

“…For any lifting-compact map <p and any lifting on the space of all bounded measurable functions on the underlying probability space, there is an associated 'lifted function' p'(<p) of <p taking values in T; p'(q>) is Borel measurable and satisfies the condition (1) is valid. The weak equivalence of <p and p'(<p) given by (1) becomes a strong equivalence in the sense that (2) p'((p) = <p /x-a.e.…”

Section: Introductionmentioning

confidence: 99%

On strong lifting compactness, with applications to topological vector spaces

1986

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The notion of strong lifting compactness is introduced for completely regular Hausdorff spaces, and its structural properties, as well as its relationship to the strong lifting, to measure compactness, and to lifting compactness, are discussed. For metrizable locally convex spaces under their weak topology, strong lifting compactness is characterized by a list of conditions which are either measure theoretical or topological in their nature, and from which it can be seen that strong lifting compactness is the strong counterpart of measure compactness in that case.

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“…On the other hand Graf has proved that strong liftings always exist for measures on second countable spaces [6]. Other positive results on the existence of strong liftings are given in [2] and [4].…”

mentioning

confidence: 97%

“…Then using (1), (2) and (3) we may easily check that θ is an upper density of < 5. Let θ' be the associated to θ lower density of <$ defined by…”

Section: Indeed Since X Is Hereditary Lindelόf [[3] Theorem 22] Evmentioning

confidence: 99%