On Systems of Independent Sets
-
Pavel Jahoda
and
Monika Jahodová
Abstract
The classical probability that a randomly chosen number from the set {n ∈ N : n ≤ n0} belongs to a set A ⊆ N can be approximated for large number n0 by the asymptotic density of the set A. We say that the events are independent if the probability of their intersection is equal to the product of their probabilities. By analogy we define the independence of sets. We say that the sets are independent if the asymptotic density of their intersection is equal to the product of their asymptotic densities. In the article is described a generalisation of one of the criteria of independence of sets and one interesting case in which sets are not independent
References
[1] JAHODA, P.-PĚLUCHOVÁ, M.: Systems of sets with multiplicative asymptotic density, Math. Slovaca 58 (2008), 393-404.10.2478/s12175-008-0083-2Search in Google Scholar
[2] JAHODA, P.-JAHODOVÁ, M.: On a set of asymptotic densities, Acta Math. Univ. Ostrav. 16 (2009), 21-30.Search in Google Scholar
[3] JAHODOVÁ, M.: Systems of independent sets. Thesis, University of Ostrava, 2011 (Czech). Search in Google Scholar
© 2015 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- The M-Regular Graph of a Commutative Ring
- Further Properties of the Lattice of Torsion Classes of Abelian Cyclically Ordered Groups
- Free Power-Commutative Groupoids
- On Systems of Independent Sets
- Note on G-Module Structure of Orders
- Semisimple Hopf Algebras of Dimension 2q3
- On the Convergence of a Mapped by a Function
- Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions
- Meromorphic Functions Sharing Pairs of Small Functions
- Sharp Inequalities for Polygamma Functions
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients
- Existence of Ground State Solutions for Hamiltonian Elliptic Systems with Gradient Terms
- Approximate Higher Ring Derivations in Non-Archimedean Banach Algebras
- Characterizations of Banach Spaces which are not Isomorphic to any of their Proper Subspaces
- Operator Inequalities Related to Q-Class Functions
- On a Class of Locally Dually Flat (α,β)–Metrics
- Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices
- A Generalization of Jakubec's Formula
