An introduction to fractal Lebesgue integral

Kalita H., Golmankhanehand A. K.

Georgian Mathematical Journal, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/gmj-2025-2067
  • Dergi Adı: Georgian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Anahtar Kelimeler: fractal calculus, fractal functions, Fractal set, generalized fractal measure
  • Van Yüzüncü Yıl Üniversitesi Adresli: Hayır

Özet

This manuscript explores various characteristics of generalized fractal measures. We expand the concept of fractal integrals in relation to step functions and examine their numerous properties. Notably, since all step functions are classified as simple functions, we apply the aforementioned generalized measure to introduce Lebesgue-type integrals, referred to as FL-integrals. Additionally, we demonstrate that all F α {F^{\alpha}} -integrable functions are FL-integrals. Lastly, we address the bounded convergence theorem within the context of fractals.