Displaying similar documents to “ On L p Space Formed by Real-Valued Partial Functions ”

On L 1 Space Formed by Real-Valued Partial Functions

Yasushige Watase, Noboru Endou, Yasunari Shidama (2008)

Formalized Mathematics

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This article contains some definitions and properties refering to function spaces formed by partial functions defined over a measurable space. We formalized a function space, the so-called L1 space and proved that the space turns out to be a normed space. The formalization of a real function space was given in [16]. The set of all function forms additive group. Here addition is defined by point-wise addition of two functions. However it is not true for partial functions. The set of partial...

On systems of null sets

K. Bhaskara Rao, R. Shortt (1999)

Colloquium Mathematicae

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

Existence of mild solutions for semilinear equation of evolution

Anna Karczewska, Stanisław Wędrychowicz (1996)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of the results obtained to control theory is also shown. The main theorem of the paper allows to characterize...

Evolution inclusions in non separable Banach spaces

Francesco Saverio De Blasi, Giulio Pianigiani (1999)

Commentationes Mathematicae Universitatis Carolinae

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We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.