Integral Denjoy-McShane Fungsi Bernilai Banach

Agus Setiawan, Prof. Dr. Ch. Rini Indrati, M.Si.; Made Tantrawan, M.Sc., Ph.D.

2025 | Tesis | S2 Matematika

Pada tesis ini dibahas mengenai integral McShane fungsi bernilai Banach dan integral Denjoy-McShane fungsi bernilai Banach pada domain $[a,b]$. Pembahasan diawali dengan menjelaskan definisi dan karakteristik integral McShane fungsi bernilai Banach, dilanjutkan dengan menjelaskan teorema kekonvergenan yang berlaku pada integral McShane fungsi bernilai Banach. Pembahasan dilanjutkan dengan menjelaskan definisi dan karakteristik integral Denjoy-McShane fungsi bernilai Banach. Lebih lanjut, dibangun teorema kekonvergenan pada integral Denjoy-McShane fungsi bernilai Banach.

This thesis explores the McShane integral of Banach-valued functions and the Denjoy-McShane integral of Banach-valued functions on the domain $[a,b]$. The discussion commences with an exposition of the definition and characteristics of the McShane integral for Banach-valued functions, followed by an examination of convergence theorems applicable to McShane integrals of Banach-valued functions. The discourse then proceeds to elucidate the definition and characteristics of the Denjoy-McShane integral for Banach-valued functions. Furthermore, the thesis develops convergence theorems for the Denjoy-McShane integral of Banach-valued functions.

Kata Kunci : integral, McShane, Denjoy-McShane, kekonvergenan