Integral Henstock-Stieltjes dan Integral Nonlinear Fungsi Baire Terbatas

MADE TANTRAWAN, Dr. Ch. Rini Indrati, M.Si.

2015 | Tesis | S2 Matematika

Pada tesis ini dibahas syarat cukup agar fungsi Baire-k terbatas terintegral Henstock-Stieltjes dan terintegral nonlinear, dengan k\in\mathbb{N}. Dengan memandang himpunan semua fungsi Baire-k terbatas, \mathfrak{bB}_k[a,b], sebagai ruang \textit{two-norm}, berhasil dibuktikan teorema representasi untuk fungsional kontinu \textit{two-norm} pada \mathfrak{bB}_k[a,b] dalam bentuk integral Henstock-Stieltjes. Lebih lanjut, dibangun teorema representasi dalam bentuk integral nonlinear untuk fungsional aditif ortogonal dan \textit{almost boundedly continuous} pada \mathfrak{bB}_k[a,b].

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\in\mathbb. By considering the space of all bounded Baire-k functions, \mathfrak{bB}_k[a,b], as a two-norm space, we prove a representation theorem for two-norm continuous linear functionals defined on \mathfrak{bB}_k[a,b] in terms of the Henstock-Stieltjes integral. Furthermore, we prove a representation theorem for orthogonally additive and almost boundedly continuous functionals on the space \mathfrak{bB}_k[a,b] is given in terms of the nonlinear integral.

Kata Kunci : fungsi Baire terbatas, integral Henstock-Stieltjes, two-norm, teorema representasi.