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Displaying 21 – 30 of 30

The s-Perron, sap-Perron and ap-McShane integrals

Joo Bong Kim, Deok Ho Lee, Woo Youl Lee, Chun-Gil Park, Jae Myung Park (2004)

Czechoslovak Mathematical Journal

In this paper, we study the s-Perron, sap-Perron and ap-McShane integrals. In particular, we show that the s-Perron integral is equivalent to the McShane integral and that the sap-Perron integral is equivalent to the ap-McShane integral.

The symmetric Choquet integral with respect to Riesz-space-valued capacities

Antonio Boccuto, Beloslav Riečan (2008)

Czechoslovak Mathematical Journal

A definition of “Šipoš integral” is given, similarly to [3],[5],[10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved.

The theory of stationary vector-valued measures over R.

P. Masani (1983)

Journal für die reine und angewandte Mathematik

The Vitali convergence theorem for the vector-valued McShane integral

Richard Reynolds, Charles W. Swartz (2004)

Mathematica Bohemica

The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in $ℝ^{n}$ given by Kurzweil and...

The weak McShane integral

Mohammed Saadoune, Redouane Sayyad (2014)

Czechoslovak Mathematical Journal

We present a weaker version of the Fremlin generalized McShane integral (1995) for functions defined on a $σ$ -finite outer regular quasi Radon measure space $(S, Σ, 𝒯, μ)$ into a Banach space $X$ and study its relation with the Pettis integral. In accordance with this new method of integration, the resulting integral can be expressed as a limit of McShane sums with respect to the weak topology. It is shown that a function $f$ from $S$ into $X$ is weakly McShane integrable on each measurable subset of $S$ if and only if...

Currently displaying 21 – 30 of 30

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Displaying 21 – 30 of 30

The s-Perron, sap-Perron and ap-McShane integrals

The symmetric Choquet integral with respect to Riesz-space-valued capacities

The theory of stationary vector-valued measures over R.

The Vitali convergence theorem for the vector-valued McShane integral

The weak McShane integral

The weak Radon-Nikodym property in Banach spaces

Topological aspects of q-regular measures

Topological rings of sets and the theory of vector measures [Book]

Topologies on Spaces of Vector-Valued Continuous Functions. II.

Transforms of Vector-Valued Functions and Measures

Currently displaying 21 – 30 of 30