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On Some Classes of Operators on C(K,X)

Ioana Ghenciu (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, Σ is the σ-algebra of Borel subsets of K, C(K,X) is the Banach space of all continuous X-valued functions (with the supremum norm), and T:C(K,X) → Y is a strongly bounded operator with representing measure m:Σ → L(X,Y). We show that if T is a strongly bounded operator and T̂:B(K,X) → Y is its extension, then T is limited if and only if its extension T̂ is limited, and that T* is completely continuous (resp. unconditionally...

On strongly Pettis integrable functions in locally convex spaces.

N. D. Chakraborty, Sk. Jaker Ali (1993)

Revista Matemática de la Universidad Complutense de Madrid

Some characterizations have been given for the relative compactness of the range of the indefinite Pettis integral of a function on a complete finite measure space with values in a quasicomplete Hausdorff locally convex space. It has been shown that the indefinite Pettis integral has a relatively compact range if the functions is measurable by seminorm. Separation property has been defined for a scalarly measurable function and it has been proved that a function with this property is integrable...

On superpositionally measurable semi-Carathéodory multifunctions

Wojciech Zygmunt (1992)

Commentationes Mathematicae Universitatis Carolinae

For multifunctions F : T × X → 2 Y , measurable in the first variable and semicontinuous in the second one, a relation is established between being product measurable and being superpositionally measurable.

On systems of null sets

K. Bhaskara Rao, R. Shortt (1999)

Colloquium Mathematicae

The collection of all sets of measure zero for a finitely additive, group-valued measure is studied and characterised from a combinatorial viewpoint.

On the cliquish, quasicontinuous and measurable selections

Milan Matejdes (1991)

Mathematica Bohemica

The purpose of this paper is the investigation of the necessary and sufficient conditions under which a given multifunctions admits a cliquish and measurable selection. Our investigation also covers the search for quasicontinuous selections for multifunctions which are continuous with respect to the generalized notion of the semi-quasicontinuity.

On the control measures of vector measures.

Baltasar Rodríguez-Salinas (2003)

RACSAM

Si Σ es una σ-álgebra y X un espacio localmente convexo se estudian las condiciones para las cuales una medida vectorial σ-aditiva γ : Σ → χ tenga una medida de control μ. Si Σ es la σ-álgebra de Borel de un espacio métrico, se obtienen condiciones necesarias y suficientes usando la τ aditividad de γ. También se dan estos resultados para las polimedidas.

On the extension of D -poset valued measures

Beloslav Riečan (1998)

Czechoslovak Mathematical Journal

A variant of Alexandrov theorem is proved stating that a compact, subadditive D -poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.

Currently displaying 301 – 320 of 542