Convergence Theorems in Interval-Valued Riemann–Lebesgue Integrability

Abstract

We provide some limit theorems for sequences of Riemann–Lebesgue integrable functions. More precisely, Lebesgue-type convergence and Fatou theorems are established. Then, these results are extended to the case of Riemann–Lebesgue integrable interval-valued multifunctions.

Keywords

• Riemann–Lebesgue integral
• interval-valued (set) multifunction
• non-additive set function
• Lebesgue theorem
• Fatou theorem