Integral-C

GALUH AYUANDRIANI H, Prof. Dr. Christiana Rini Indrati, M.Si.

2023 | Tesis | MAGISTER MATEMATIKA

Dalam tesis ini dibahas mengenai suatu integral yang mengintegralkan semua fungsi terintegral Lebesgue dan derivatif dari suatu fungsi terdiferensial. Integral tersebut dikenal sebagai integral-C. Selanjutnya, dibahas sifat-sifat fungsi terintegral-C. Primitif fungsi integral-C dapat didekomposisi menjadi jumlahan fungsi terintegral Lebesgue dan derivatif dari suatu fungsi terdiferensial. Himpunan semua primitif fungsi integral-C dinotasikan dengan himpunan $\left<AC,\Delta\right>$. Selanjutnya, dibahas karakteristik primitif fungsi terintegral-C. Setiap fungsi terintegral Lebesgue merupakan fungsi terintegral-C.

In this thesis, we discuss an integral that integrates all Lebesgue integrable functions and the derivatives of a differentiable function. The integral is known as the C-integral. Then, we discuss the properties of C-integrable function. The primitive of C-integrable function can be decomposed into a sum of a Lebesgue integrable function and a derivative of a differentiable function. The set of all primitive for the C-integral is denoted by $\left<AC,\Delta\right>$. Then, we discuss the primitive characteristics of C-integrable functios. Every Lebesgue integrable functions is C-integrable functios.

Kata Kunci : integral-C, himpunan $\left<AC,\Delta\right>$, himpunan $AC$, integral Lebesgue/the C-integral, the set of $\left<AC,\Delta\right>$, the set of $AC$, the Lebesgue integral