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Displaying 21 – 40 of 88

On continuity of measurable group representations and homomorphisms

Yulia Kuznetsova (2012)

Studia Mathematica

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space ℒ(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to ℒ(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.

On c-sets and products of ideals

Marek Balcerzak (1991)

Colloquium Mathematicae

Let X, Y be uncountable Polish spaces and let μ be a complete σ-finite Borel measure on X. Denote by K and L the families of all meager subsets of X and of all subsets of Y with μ measure zero, respectively. It is shown that the product of the ideals K and L restricted to C-sets of Selivanovskiĭ is σ-saturated, which extends Gavalec's results.

On extensions of measures

K. P. S. Bhaskara Rao, B. V. Rao (1987)

Colloquium Mathematicae

On extensions of $σ$ -fields of sets

Edward Grzegorek (1993)

Acta Universitatis Carolinae. Mathematica et Physica

On fields and ideals connected with notions of forcing

W. Kułaga (2006)

Colloquium Mathematicae

We investigate an algebraic notion of decidability which allows a uniform investigation of a large class of notions of forcing. Among other things, we show how to build σ-fields of sets connected with Laver and Miller notions of forcing and we show that these σ-fields are closed under the Suslin operation.

On Haar null sets

Sławomir Solecki (1996)

Fundamenta Mathematicae

We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-locally-compact groups.) Thus we obtain the following characterization of locally compact, abelian groups: Let...

On $I$ -continuity and $I$ -semicontinuity points

Tomasz Natkaniec (1986)

Mathematica Slovaca

On ideals with projective bases.

Cichón, J., Kharazishvili, A. (2002)

Georgian Mathematical Journal

On injective holomorphic Fredholm mappings of index 0 in complex Banach spaces

Dietmar Abts (1980)

Commentationes Mathematicae Universitatis Carolinae

On intersections of sets of positive Lebesgue measure

J. Cichoń, A. Szymański, B. Węglorz (1987)

Colloquium Mathematicae

On intersections of small perfect sets.

Fast, H. (2002)

Georgian Mathematical Journal

On Kantorovich's result on the symmetry of Dini derivatives

Martin Koc, Luděk Zajíček (2010)

Commentationes Mathematicae Universitatis Carolinae

For $f : (a, b) \to ℝ$ , let $A_{f}$ be the set of points at which $f$ is Lipschitz from the left but not from the right. L.V. Kantorovich (1932) proved that, if $f$ is continuous, then $A_{f}$ is a “( $k_{d}$ )-reducible set”. The proofs of L. Zajíček (1981) and B.S. Thomson (1985) give that $A_{f}$ is a $σ$ -strongly right porous set for an arbitrary $f$ . We discuss connections between these two results. The main motivation for the present note was the observation that Kantorovich’s result implies the existence of a $σ$ -strongly right porous set $A \subset (a, b)$ ...

On Marczewski-Burstin representable algebras

Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)

Colloquium Mathematicae

We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.

On Measurability of Uncountable Unions of Measurable Sets

Alexander Abian, Paula Kemp (1992)

Publications de l'Institut Mathématique

On measure zero sets in topological vector spaces.

Grinč, M. (1996)

Acta Mathematica Universitatis Comenianae. New Series

On minimal generators of σ-fields

Bohdan Aniszczyk, Ryszard Frankiewicz (1984)

Fundamenta Mathematicae

On nonmeasurable images

Robert Rałowski, Szymon Żeberski (2010)

Czechoslovak Mathematical Journal

Let $(X, 𝕀)$ be a Polish ideal space and let $T$ be any set. We show that under some conditions on a relation $R \subseteq T^{2} \times X$ it is possible to find a set $A \subseteq T$ such that $R (A^{2})$ is completely $𝕀$ -nonmeasurable, i.e, it is $𝕀$ -nonmeasurable in every positive Borel set. We also obtain such a set $A \subseteq T$ simultaneously for continuum many relations ${(R_{α})}_{α < 2^{ω}} .$ Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.

On nonmeasurable selectors of countable group actions

Piotr Zakrzewski (2009)

Fundamenta Mathematicae

Given a set X, a countable group H acting on it and a σ-finite H-invariant measure m on X, we study conditions which imply that each selector of H-orbits is nonmeasurable with respect to any H-invariant extension of m.

On nonmeasurable subgroups of the real line.

Kharazishvili, A.B. (1996)

Journal of Applied Analysis

On nonparadoxical sets

Marcin Penconek (1991)

Fundamenta Mathematicae

Currently displaying 21 – 40 of 88

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