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On non-additive probability measures

  • Beloslav Riečan EMAIL logo and Karol Samuelčik
Published/Copyright: November 30, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 6

Abstract

The additivity of considered measures or integrals resp. can be omitted in some problems of mathematical analysis and its applications. In the paper it is shown that similar situations are possible also in the probability theory. As an example is proved a generalized version of the central limit theorem about the convergence of arithmetical means of independent random variables to the Gauss distribution.

MSC 2010: Primary 60A10; 60F05
Keywords: subadditive probability measure; central limit theorem
Dedicated to Professor Paolo de Lucia on the occasion of his 80th birthday

Communicated by Anatolij Dvurečenskij

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Received: 2016-5-12
Accepted: 2016-8-25
Published Online: 2017-11-30
Published in Print: 2017-11-27

© 2017 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  2. Paolo de Lucia
  4. Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
  6. A note on field-valued measures
  8. Topologies and uniformities on d0-algebras
  10. On some properties of 𝓙-approximately continuous functions
  12. Porous subsets in the space of functions having the Baire property
  14. Rademacher’s theorem in Banach spaces without RNP
  16. Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
  18. Measure games on pseudo-D-lattices
  20. On some properties of k-subadditive lattice group-valued capacities
  22. Lp Spaces in vector lattices and applications
  24. The Choquet integral with respect to fuzzy measures and applications
  26. A note on the range of vector measures
  28. Ideal convergent subsequences and rearrangements for divergent sequences of functions
  30. Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
  32. A generalization of the exponential sampling series and its approximation properties
  34. Monotonicity and total boundedness in spaces of “measurable” functions
  36. Vector lattices in synaptic algebras
  38. Density, ψ-density and continuity
  40. Feather topologies
  42. On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
  44. Rate of convergence of empirical measures for exchangeable sequences
  46. On non-additive probability measures
  48. Equi-topological entropy curves for skew tent maps in the square
  50. On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
https://doi.org/10.1515/ms-2017-0071
Keywords for this article
subadditive probability measure; central limit theorem

Articles in the same Issue

  2. Paolo de Lucia
  4. Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
  6. A note on field-valued measures
  8. Topologies and uniformities on d0-algebras
  10. On some properties of 𝓙-approximately continuous functions
  12. Porous subsets in the space of functions having the Baire property
  14. Rademacher’s theorem in Banach spaces without RNP
  16. Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
  18. Measure games on pseudo-D-lattices
  20. On some properties of k-subadditive lattice group-valued capacities
  22. Lp Spaces in vector lattices and applications
  24. The Choquet integral with respect to fuzzy measures and applications
  26. A note on the range of vector measures
  28. Ideal convergent subsequences and rearrangements for divergent sequences of functions
  30. Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
  32. A generalization of the exponential sampling series and its approximation properties
  34. Monotonicity and total boundedness in spaces of “measurable” functions
  36. Vector lattices in synaptic algebras
  38. Density, ψ-density and continuity
  40. Feather topologies
  42. On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
  44. Rate of convergence of empirical measures for exchangeable sequences
  46. On non-additive probability measures
  48. Equi-topological entropy curves for skew tent maps in the square
  50. On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
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