COMPARISON OF THE RIEMANN INTEGRAL AND THE LEBESGUE INTEGRAL
Keywords:
Riemann integral, Lebesgue integral, measure theory, continuity, boundedness, probability theory, mathematical analysis.Abstract
This paper discusses the concepts of the Riemann and Lebesgue integrals, their fundamental differences, and their mathematical analysis. While the Riemann integral is studied as a traditional approach to integration, the Lebesgue integral is more closely related to measure theory. This paper examines the definitions, advantages, and disadvantages of both integrals, as well as their areas of application.
References
.Riemann, B. (1854). "Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe."
.Lebesgue, H. (1902). "Intégrale, longueur, aire."
.Rudin, W. (1976). "Principles of Mathematical Analysis." McGraw-Hill.
.Folland, G. B. (1999). "Real Analysis: Modern Techniques and Their Applications." Wiley.
.Bartle, R. G. (1995). "The Elements of Integration and Lebesgue Measure." Wiley.
.Kolmogorov, A. N., & Fomin, S. V. (1975). "Introductory Real Analysis." Dover.
.Royden, H. L. (1988). "Real Analysis." Macmillan.
.Zygmund, A. (2002). "Trigonometric Series." Cambridge University Press.
.Lang, S. (2012). "Real and Functional Analysis." Springer.
.Hewitt, E., & Stromberg, K. (1975). "Real and Abstract Analysis." Springer.
