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Article

Výborný, Rudolf
Kurzweil’s PU integral as the Lebesgue integral. (English). Mathematica Bohemica, vol. 131 (2006), issue 1, pp. 11-14
MSC: 26A39, 26A42, 28A99 | MR 2210999 | Zbl 1112.26013 | DOI: 10.21136/MB.2006.134077
Keywords:
Kurzweil’s PU integral; Lebesgue integral; McShane integral
Summary:
For a merely continuous partition of unity the PU integral is the Lebesgue integral.
References:
[1] Russel A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. American Mathematical Society, 1994. MR 1288751
[2] J. Kurzweil, J. Jarník: A non absolutely convergent integral which admits transformation and can be used on manifolds. Czechoslovak Math. J. 35 (1985), 116–139. MR 0779340
[3] J. Kurzweil, J. Jarník: A new and more powerful concept of the PU integral. Czechoslovak Math. J. 38 (1988), 8–48. MR 0925939
[4] J. Kurzweil, J. Mawhin, W. Pfeffer: An integral defined by approximating BV partitions of unity. Czechoslovak Math. J. 41 (1991), 695–712. MR 1134958
[5] Lee, Peng Yee, Rudolf Výborný: The Integral: An Easy Approach after Kurzweil and Henstock. Cambridge University Press, Cambridge, UK, 2000. MR 1756319
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