INTEGRAL HENSTOCK-STIELTJES DAN INTEGRAL NONLINEAR FUNGSI BAIRE TERBATAS ( THE HENSTOCK-STIELTJES INTEGRAL AND THE NONLINEAR INTEGRAL OF BOUNDED BAIRE FUNCTIONS )

Tantrawan, Made, Rini Indrati

2015 | Disertasi | FMIPA

In this thesis, we give sufficient conditions for bounded Baire-k functions to be integrable in the sense of the Henstock-Stieltjes integral and the nonlinear integral, where k 2 N. By considering the space of all bounded Baire-k functions, bBk[a; b], as a two-norm space, we prove a representation theorem for two-norm continuous linear functionals defined on bBk[a; b] in terms of the Henstock-Stieltjes integral. Furthermore, a representation theorem for orthogonally additive and almost boundedly continuous functionals on the space bBk[a; b] is given in terms of the nonlinear integral.

Kata Kunci : N