Page 1

Displaying 1 – 6 of 6

Showing per page

The Denjoy extension of the Riemann and McShane integrals

Jae Myung Park (2000)

Czechoslovak Mathematical Journal

In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval a , b into a Banach space X . It is shown that a Denjoy-Bochner integrable function on a , b is Denjoy-Riemann integrable on a , b , that a Denjoy-Riemann integrable function on a , b is Denjoy-McShane integrable on a , b and that a Denjoy-McShane integrable function on a , b is Denjoy-Pettis integrable on a , b . In addition, it is shown that for spaces that do not contain a copy of c 0 , a measurable Denjoy-McShane integrable...

The (sub/super)additivity assertion of Choquet

Heinz König (2003)

Studia Mathematica

The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper...

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.

Currently displaying 1 – 6 of 6

Page 1