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57
MAHARAM ALGEBRAS AND COHEN REALS
, 2007
"... We show that the product of any two nonatomic Maharam algebras adds a Cohen real. As a corollary of this and a result of Shelah (1994) we obtain that the product of any two nonatomic ccc Souslin forcing notions adds a Cohen real. ..."
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We show that the product of any two nonatomic Maharam algebras adds a Cohen real. As a corollary of this and a result of Shelah (1994) we obtain that the product of any two nonatomic ccc Souslin forcing notions adds a Cohen real.
Maharam Algebras
, 2008
"... Maharam algebras are complete Boolean algebras carrying a positive continuous submeasure. They were introduced and studied by Maharam in [24] in relation to Von Neumann’s problem on the characterization of measure algebras. The question whether every Maharam algebra is a measure algebra has been the ..."
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Maharam algebras are complete Boolean algebras carrying a positive continuous submeasure. They were introduced and studied by Maharam in [24] in relation to Von Neumann’s problem on the characterization of measure algebras. The question whether every Maharam algebra is a measure algebra has been
MAHARAM TRACES ON VON NEUMANN ALGEBRAS
, 905
"... Abstract. Traces Φ on von Neumann algebras with values in complex order complete vector lattices are considered. The full description of these traces is given for the case when Φ is the Maharam trace. The version of RadonNikodymtype theorem for Maharam traces is established. ..."
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Abstract. Traces Φ on von Neumann algebras with values in complex order complete vector lattices are considered. The full description of these traces is given for the case when Φ is the Maharam trace. The version of RadonNikodymtype theorem for Maharam traces is established.
THE CLASSIFICATION PROBLEM FOR NONATOMIC WEAK Lp SPACES
"... Abstract. The aim of the paper is to study the isomorphic structure of the weak Lp space Lp,∞(Ω,Σ, µ) when (Ω,Σ, µ) is a purely nonatomic measure space. Using Maharam’s classification of measure algebras, it is shown that every such Lp,∞(Ω,Σ, µ) is isomorphic to a weak Lp space defined on a weighted ..."
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Abstract. The aim of the paper is to study the isomorphic structure of the weak Lp space Lp,∞(Ω,Σ, µ) when (Ω,Σ, µ) is a purely nonatomic measure space. Using Maharam’s classification of measure algebras, it is shown that every such Lp,∞(Ω,Σ, µ) is isomorphic to a weak Lp space defined on a
Maharam Spectra of Loeb Spaces
 The Journal of Symbolic Logic
"... We characterize Maharam spectra of Loeb probability spaces and give some applications of the results. 0. Introduction In the nonstandard approach to probability theory, a central role is played by a family of very rich probability spaces, known as Loeb spaces. It is natural to ask for a description ..."
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description of the Loeb spaces, or at least a description of their measure algebras, in standard terms. By Maharam's Theorem (see x1), the measure algebra of any atomless probability space(\Omega ; B; ) is determined up to isomorphism by a finite or countable set of "weighted" infinite
Special Subsets of cf(µ) µ, Boolean Algebras and Maharam measure Algebras
, 1998
"... The original theme of the paper is the existence proof of “there is ¯η = 〈ηα: α < λ 〉 which is a (λ, J)sequence for Ī = 〈Ii: i < δ〉, a sequence of ideals. This can be thought of as in a generalization to Luzin sets and Sierpinski sets, but for the product ∏ i<δ dom(Ii), the existence proof ..."
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Cited by 14 (13 self)
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proofs are related to pcf. The second theme is when does a Boolean algebra B has free caliber λ (i.e. if X ⊆ B and X  = λ, then for some Y ⊆ X with Y  = λ and Y is independent). We consider it for B being a Maharam measure algebra, or B a (small) product of free Boolean algebras, and κcc Boolean
Between Maharam’s and von Neumann’s problems
, 2004
"... In the context of definable algebras Maharam’s and von Neumann’s problems essentially coincide. Consequently, random forcing is the only definable ccc forcing adding a single real that does not make the ground model reals null, and the only pairs of definable ccc σideals with the Fubini property ar ..."
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Cited by 7 (1 self)
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In the context of definable algebras Maharam’s and von Neumann’s problems essentially coincide. Consequently, random forcing is the only definable ccc forcing adding a single real that does not make the ground model reals null, and the only pairs of definable ccc σideals with the Fubini property
(II) Knaster property (III) Exhaustive functional (IV) Supermeasure. (V) Exhaustive submeasure Ã (Vc) Maharam algebras
, 2007
"... We deal with classes of Boolean algebras (BA) and partial orders that carry strictly positive exhaustive functionals, i.e. a mapping f: B → R+ such that f(a) = 0 iff a = 0 and for any disjoint sequence 〈an: n ∈ ω 〉 lim f(an) = 0. Notation. Hierarchy of clasess of BA’s is: (I) ccc ..."
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We deal with classes of Boolean algebras (BA) and partial orders that carry strictly positive exhaustive functionals, i.e. a mapping f: B → R+ such that f(a) = 0 iff a = 0 and for any disjoint sequence 〈an: n ∈ ω 〉 lim f(an) = 0. Notation. Hierarchy of clasess of BA’s is: (I) ccc
ON THE ISOMORPHISM PROBLEM FOR MEASURES ON BOOLEAN ALGEBRAS
"... Abstract. The paper investigates possible generalisations of Maharam’s theorem to a classification of Boolean algebras that support a finitely additive measure. We prove that Boolean algebras that support a finitely additive nonatomic uniformly regular measure are metrically isomorphic to a subalge ..."
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Abstract. The paper investigates possible generalisations of Maharam’s theorem to a classification of Boolean algebras that support a finitely additive measure. We prove that Boolean algebras that support a finitely additive nonatomic uniformly regular measure are metrically isomorphic to a
COMPLETE CCC BOOLEAN ALGEBRAS, THE ORDER SEQUENTIAL TOPOLOGY, AND A PROBLEM Of Von Neumann
, 2005
"... Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B,τs) is topologically dense. 2. It is consistent that every weakly distributive complete cc ..."
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Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B,τs) is topologically dense. 2. It is consistent that every weakly distributive complete
Results 1  10
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57