A Brief Introduction to Henstock Kurzweil Integral
3rd International E-Conference on Mathematical Advances and Applications, İstanbul, Türkiye, 24 - 27 Haziran 2020, ss.119, (Özet Bildiri)
- Yayın Türü: Bildiri / Özet Bildiri
- Basıldığı Şehir: İstanbul
- Basıldığı Ülke: Türkiye
- Sayfa Sayıları: ss.119
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
Henstock-Kurzweil integral, known as gauge integral or generalized Riemann integral, is defined based on the modified Riemann sum. It extends the Lebesgue integral so that it has a wider class of integrable functions. That is, the Lebesgue integrability implies Henstock-Kurzweil integrability, however the converse is not necessarily true. Furthermore, it has some applications in mathematics, computer science and engineering. In this work, we examine the Henstock-Kurzweil integral and present its fundamental properites and some examples, especially functions that are Henstock-Kurzweil integrable but not Lebesgue integrable. Finally, we study the relationship between Henstock-Kurzweil integral and Lebesgue integral.