## On the Kluvánek construction of the Lebesgue integral.(English)Zbl 1292.28007

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.

### MSC:

 28A25 Integration with respect to measures and other set functions
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### References:

 [1] Boccuto A., Riečan B., Vrábelová M.: Kurzweil-Henstock Integral in Riesz Spaces. Betham, 2009. [2] Kluvánek, I.: Archimedes was right. Elemente der Mathematik 42, 3 (1987), 51-82. · Zbl 0706.26005 [3] Kluvánek, I.: Archimedes was right. Elemente der Mathematik 42, 4 (1987), 83-114. · Zbl 0706.26005 [4] Kluvánek, I.: Integral Calculus. UK, Ružomberok, 2011 · Zbl 0779.28004 [5] Riečan, B.: On Probability and Measure. Alfa, Bratislava, 1971 · Zbl 0205.07203 [6] Riečan, B., Neubrunn T.: Integral, Measure, and Ordering. Kluwer, Dordrecht, 1997. · Zbl 0916.28001 [7] Riečan, B., Tkáčik, Š.: A note on the Kluvánek integral. Tatra Mt. Math. Publ 49 (2011), 59-65. · Zbl 1265.26018 [8] Šipoš, J.: Integral representation of nonlinear functionals. Math. Slovaca 29 (1979), 333-346.
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