Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

The Egoroff Theorem for Riesz Space-valued Monotone Measures

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Some Results on Boundedness in Locally Convex Cones

Locally convex cones and the Schröder-Simpson Theorem

At MFPS 23 at Birmingham, Schröder and Simpson had announced a result that I did not absorb at the time. A special case of that theorem for stably compact spaces was announced by Cohen, Escardo and the author shortly afterwards. I did not believe in the theorem of Schröder and Simpson until I saw a proof that they showed to me in detail during a visit to Edinburgh. At the New Interactions Works...

On measures of size for convex cones

By using an axiomatic approach we formalize the concept of size index for closed convex cones in the Euclidean space R. We review a dozen of size indices disseminated through the literature, commenting on the advantages and disadvantages of each choice. Mathematics Subject Classification: 28A75, 51M25, 52A20, 52A40.

some results on boundedness in locally convex cones