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Pointwise density topology

Magdalena Górajska (2015)

Open Mathematics

The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density...

Positive operator bimeasures and a noncommutative generalization

Kari Ylinen (1996)

Studia Mathematica

For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of...

Pure measures

Zdeněk Frolík, Jan K. Pachl (1973)

Commentationes Mathematicae Universitatis Carolinae

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