Limits of families of measure algebras

Joji Takahashi

Displaying similar documents to “Limits of families of measure algebras”

A new proof of Kelley's Theorem

S. Ng (1991)

Fundamenta Mathematicae

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Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.

Properties of forcing preserved by finite support iterations

Miroslav Repický (1991)

Commentationes Mathematicae Universitatis Carolinae

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We shall investigate some properties of forcing which are preserved by finite support iterations and which ensure that unbounded families in given partially ordered sets remain unbounded.

Non-trivial derivations on commutative regular algebras.

A. F. Ber, Vladimir I. Chilin, Fyodor A. Sukochev (2006)

Extracta Mathematicae

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Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra...

Cellularity of free products of Boolean algebras (or topologies)

Saharon Shelah (2000)

Fundamenta Mathematicae

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The aim this paper is to present an answer to Problem 1 of Monk [10], [11]. We do this by proving in particular that if μ is a strong limit singular cardinal, $θ = {(2^{c f (μ)})}^{+}$ and $2^{μ} = μ^{+}$ then there are Boolean algebras $𝔹_{1}, 𝔹_{2}$ such that $c (𝔹_{1}) = μ, c (𝔹_{2}) < θ b u t c (𝔹_{1} * 𝔹_{2}) = μ^{+}$ . Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if $𝔹$ is a ccc Boolean algebra and $μ^{ℶ_{ω}} \leq λ = c f (λ) \leq 2^{μ}$ then $𝔹$ satisfies the λ-Knaster condition (using the “revised GCH theorem”).

Minimax inequality for a special class of functionals and its application to existence of three solutions for a Dirichlet problem in one-dimensional case.

Afrouzi, G.A., Heidarkhani, S., Hossienzadeh, H., Yazdani, A. (2010)

The Journal of Nonlinear Sciences and its Applications

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Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms.

Ono, Takayori (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Lectures on cylindric set algebras

J. Monk (1993)

Banach Center Publications

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On lifting quasi-Radon measures.

Malyugin, S.A. (2001)

Sibirskij Matematicheskij Zhurnal

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Stability of the 4-2 Binary Addition Circuit Cells. Part I

Katsumi Wasaki (2008)

Formalized Mathematics

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To evaluate our formal verification method on a real-size calculation circuit, in this article, we continue to formalize the concept of the 4-2 Binary Addition Cell primitives (FTAs) to define the structures of calculation units for a very fast multiplication algorithm for VLSI implementation [11]. We define the circuit structure of four-types FTAs, TYPE-0 to TYPE-3, using the series constructions of the Generalized Full Adder Circuits (GFAs) that generalized adder to have for each positive...