Integral Denjoy

SIGIT SYAIFULLOH, Prof. Dr. Christiana Rini Indrati, M.Si.

2024 | Skripsi | MATEMATIKA

Pada tugas akhir ini akan dijelaskan tentang integral Denjoy pada interval [a,b]. Pembahasan dimulai dengan pembahasan fungsi kontinu mutlak teritlak kuat pada [a,b] dan sifat hampir di mana-mana pada [a,b]. Pada pembahasan integral Denjoy, disampaikan sifat-sifat fungsi terintegral Denjoy, seperti sifat linearitas, sifat monoton, sifat aditif fungsi terintegral Denjoy pada [a,b], dan hubungan fungsi terintegral Denjoy pada [a,b] dengan fungsi terintegral Riemann pada [a,b]. Selanjutnya, pada bagian akhir tugas akhir ini disampaikan teorema kekonvergenan integral Denjoy pada [a,b].

In this final project, it will be discused the Denjoy integral on the interval [a,b]. The discussion will be started by discussing the generalized absolutely continuous in the restricted sense on [a,b] and derivative almost everywhere on [a,b]. In the discussion of the Denjoy integral, the properties of the Denjoy integrable functions are presented, such as the linearity property, the monotone property, the additively of the Denjoy integrable functions on [a,b], and the relationship between the Denjoy integrable functions on [a,b] and the Riemann integrable functions on [a,b]. Finally, in this final project, will be discused the convergence theorem of Denjoy integral on [a,b].

Kata Kunci : Integral Riemann, Integral Denjoy, Teorema Kekonvergenan,