Lebesgue Measure and Integration on Subsets of R^d
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Page Numbers:
15-26
Digital Object Identifier:
10.58578/mjms.v3i1.3958
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Authors:
Nand Kishor Kumar1*, Chudamani Pokhrel2, Dipendra Prasad Yadav3 
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Authors retain copyright and grant the journal right of first publication.
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Abstract
Henri Lebesgue, a French mathematician, discovered centuries ago that the Riemann Integral does not work well on unbounded functions. It prompts him to consider another way to integration known as Lebesgue Integral. This paper discusses the Riemann integral's shortcomings and introduce a more thorough concept of integration, the Lebesgue integral, repeated integration. There is also some debate about the Lebesgue measure, which determines the Lebesgue integral. Some examples are given, such as F_σ -set, G_δ -set and Cantor function. In this article, we first look into a unified theory for d-dimensional volume based on the concept of a measure, and then we will use that theory to build a stronger and more flexible theory for integration.
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References
The term volume is also used, more strictly, as a synonym of 3-dimensional volume
Lebesgue, H. (1902). Integral Longueur, Aire, Annali di Matematica Pura ed Applicata. 7: 231–359. doi:10.1007/BF02420592. S2CID 121256884.
Bartle, Robert G. (1995). The elements of integration and Lebesgue measure. Wiley Classics Library. New York: John Wiley & Sons Inc. xii+179. ISBN 0-471-04222-6. MR 1312157.
Lebesgue, H. (1904). Leçons sur l'intégration et la recherche des functions primitives". Lecons,2, Paris: Gauthier-Villars.
Heil, C. (2019). Introduction to Real Analysis, Springer, Cham, 17,1-480.
Stein. E.M. & Shakarchi, R. (2005). Real Analysis. NJ: Princeton University Press
Wheeden. R.L. & Zygmund, A. (1977). Measure and Integral. New York: Marcel Dekker.
Folland, G. B. (1999). Real Analysis, New York: Wiley, 2, 1-387.
Kesavan, S. (2019). Measure and Integration. Springer Singapore,1, 1-232.
William F. (2009). Trench. Introduction to real analysis.
Russell A. G. (1994). The integrals of Lebesgue, Denjoy, Perron, and Henstock, 4. Ameri. Math. Soc.
Dennis D. W. (2008). William Mendenhall, and Richard L. Scheaffer. Mathematical statistics with applications. Brooks-Cole.
Interactive real analysis. http://www.mathcs.org/analysis/reals/. Accessed: 2017-05-10.
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