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Article

Riečan, Beloslav
On the Kluvánek Construction of the Lebesgue Integral. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 52 (2013), issue 2, pp. 99-105
MSC: 28A25 | MR 3202383 | Zbl 06296018
Keywords:
Lebesgue integral; rings of sets; measures on compact interval
Summary:
I. Kluvánek suggested to built the Lebesgue integral on a compact interval in the real line by the help of the length of intervals only. In the paper a modification of the Kluvánek construction is presented applicable to abstract spaces, too.
References:
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[3] Kluvánek, I.: Archimedes was right. Elemente der Mathematik 42, 4 (1987), 83–114. MR 0896118 | Zbl 0706.26005
[4] Kluvánek, I.: Integral Calculus. UK, Ružomberok, 2011 (in Slovak).
[5] Riečan, B.: On Probability and Measure. Alfa, Bratislava, 1971 (in Slovak).
[6] Riečan, B., Neubrunn T.: Integral, Measure, and Ordering. Kluwer, Dordrecht, 1997. MR 1489521 | Zbl 0916.28001
[7] Riečan, B., Tkáčik, Š.: A note on the Kluvánek integral. Tatra Mt. Math. Publ 49 (2011), 59–65. MR 2865796 | Zbl 1265.26018
[8] Šipoš, J.: Integral representation of nonlinear functionals. Math. Slovaca 29 (1979), 333–346. MR 0562006
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