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Lp Spaces in vector lattices and applications

  • Antonio Boccuto EMAIL logo , Domenico Candeloro und Anna Rita Sambucini
Veröffentlicht/Copyright: 30. November 2017
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 67 Heft 6

Abstract

Lp spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian motion and the Brownian bridge are studied, to solve some stochastic differential equations.

MSC 2010: 28B15; 41A35; 46G10
Keywords: vector lattice; filter convergence; modular; Lp space; Hermite-Hadamard inequality; Schwartz inequality; Jensen inequality; Brownian motion

This work was supported by University of Perugia - Department of Mathematics and Computer Sciences - Grant Nr 2010.011.0403 and by the Grant prot. UFMBAZ2017/0000326 of GNAMPA - INDAM (Italy).

A. Boccuto orcid id: 0000-0003-3795-8856, D. Candeloro orcid id: 0000-0003-0526-5334, A. R. Sambucini orcid id: 0000-0003-0161-8729.

Dedicated to Professor Paolo de Lucia on the occasion of his 80th birthday

Communicated by Anatolij Dvurečenskij

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Received: 2016-3-16
Accepted: 2016-5-1
Published Online: 2017-11-30
Published in Print: 2017-11-27

© 2017 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  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-2017-0060
Schlagwörter für diesen Artikel
vector lattice; filter convergence; modular; Lp space; Hermite-Hadamard inequality; Schwartz inequality; Jensen inequality; Brownian motion

Artikel in diesem Heft

  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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