Generalized Lebesgue integral

Authors:
Qiang Zhang;Radko Mesiar;Jun Li;Peter Struk
Affiliations:
School of Management and Economics, Beijing Institute of Technology, Beijing 100081, People's Republic of China;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368 Bratislava, Slovakia and Institute for Research and Applications of Fuzz ...;School of Science, Communication University of China, Beijing 100024, People's Republic of China;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368 Bratislava, Slovakia
Venue:
International Journal of Approximate Reasoning
Year:
2011

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Abstract

A new definition of integral-like functionals exploiting the ideas of the Lebesgue integral construction and extending the idea of pan-integrals is given. Some convergence theorems for sequence of measurable functions are discussed. As a result, a theoretical basis for applications of the generalized Lebesgue integral is provided. Several types of integrals known from the literature are shown to be special cases of generalized Lebesgue integral.