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Super Level Measures: Averaging Before Integrating

  • Conference paper
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New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

In many situations, such as the definition of the essential supremum, or definition of \(L_p\)-norms, or the weak type estimates of the Hardy-Littlewood operator, or the construction of certain nonadditive integrals, etc.

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References

  1. Borzová, J., Halčinová, L., Šupina, J.: Size and standard super level measure. In: Medina, J., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems: Theory and Foundations, IPMU 2018. Communications in Computer and Information Science, vol. 853, pp. 219–230. Springer, Cham (2018)

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  2. Do, Y., Thiele, C.: \(L^p\) theory for outer measures and two themes of Lennart Carleson united. Bull. Am. Math. Soc. 52(2), 249–296 (2015)

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  3. Halčinová, L., Hutník, O., Kiseľák, J., Šupina, J.: Beyond the scope of super level measures. Fuzzy Sets Syst. 364, 36–63 (2019). https://doi.org/10.1016/j.fss.2018.03.007

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Acknowledgments

This work was supported by the Slovak Research and Development Agency under the contract No. APVV-16-0337.

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Correspondence to Ondrej Hutník .

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Hutník, O. (2019). Super Level Measures: Averaging Before Integrating. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_3

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