Integral Henstock-Stieltjes Fungsi Bernilai Hilbert ( The Henstock-Stieltjes Integral of Hilbert Valued Function )

MADE BENNY PRASETYA WIRANATA, Ch. Rini Indrati, M.Si., Dr.

2015 | Skripsi | S1 MATEMATIKA

Di dalam tugas akhir ini dibahas definisi dan karakteristik integral Henstock-Stieltjes fungsi bernilai Hilbert X. Pembahasan dimulai dengan memberikan definisi dan karakteristik fungsi teregulasi, fungsi bervariasi terbatas dan fungsi kontinu mutlak dari [a, b] ke ruang Hilbert X. Selanjutnya, berdasarkan fungsi hasil kali dalam pada ruang Hilbert X, didefinisikan integral Henstock-Stieltjes fungsi bernilai Hilbert X. Pada bagian akhir, diberikan sifat integral Henstock-Stieltjes fungsi bernilai Hilbert X dan karakteristik primitif integral Henstock-Stietjes fungsi bernilai Hilbert X.

In this final project, we discuss about definition and some characteristics of Henstock-Stieltjes integral of Hilbert X valued function. First, we begin with definition and some characteristics of regulated function, bounded variation function and absolute continuous function on [a, b] with values in Hilbert space X. According to inner product function in Hilbert space X, we define Henstock-Stieltjes integral of Hilbert X valued function. In the end, we give some properties of Henstock-Stieltjes integral of Hilbert X valued function and the characteristics of it's primitif.

Kata Kunci : Integral Henstock-Stieltjes