Displaying similar documents to “A note on Lusin measurability in measure spaces”

Structure of measures on topological spaces.

José L. de María, Baltasar Rodríguez Salinas (1989)

Revista Matemática de la Universidad Complutense de Madrid

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The Radon spaces of type (T), i.e., topological spaces for which every finite Borel measure on Omega is T-additive and T-regular are characterized. The class of these spaces is very wide and in particular it contains the Radon spaces. We extend the results of Marczewski an Sikorski to the sygma-metrizable spaces and to the subsets of the Banach spaces endowed with the weak topology. Finally, the completely additive families of measurable subsets related with the works of Hansell, Koumoullis,...

Negligible sets and good functions on polydiscs

Kohur Gowrisankaran (1979)

Annales de l'institut Fourier

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A notion of negligible sets for polydiscs is introduced. Some properties of non-negligible sets are proved. These results are used to construct good and good inner functions on polydiscs.

Spaces of measurable functions

Piotr Niemiec (2013)

Open Mathematics

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For a metrizable space X and a finite measure space (Ω, 𝔐 , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of 𝔐 -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point. ...

Integral representation for a class of multiply superharmonic functions

Kohur Gowrisankaran (1973)

Annales de l'institut Fourier

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Let Ω 1 , ... , Ω n be harmonic spaces of Brelot with countable base of completely determining domains. The elements of a subcone C of the cone of positive n -superharmonic functions in Ω 1 × ... × Ω n is shown to have an integral representation with the aid of Radon measures on the extreme elements belonging to a compact base of C . The extreme elements are shown to be the product of extreme superharmonic functions on the component spaces and the measure representing each element is shown to be unique. Necessary...