Probabilistic norms and convergence of random variables

DOI10.1016/S0022-247X(02)00577-2zbMath1020.60018OpenAlexW2000675160MaRDI QIDQ1874427

Bernardo Lafuerza-Guillén, Carlo Sempi

Publication date: 25 May 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00577-2

zbMATH Keywords

complete convergencealmost sure convergenceconvergence in probabilityprobabilistic normed spaceprobabilistic form

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Probability theory on algebraic and topological structures (60B99) Limit theorems in probability theory (60F99) Functional analysis in probabilistic metric linear spaces (46S50)

Related Items (11)

Weighted modulus \(S_\theta\)-convergence of order \(\alpha\) in probability ⋮ SOME PROPERTIES OF THE SET OF ALL STRONG UNIFORM CLUSTER POINTS ⋮ Statistical \(\Lambda\)-convergence in probabilistic normed spaces ⋮ The Bishop-Phelps theorem in complete random normed modules endowed with the (\(\varepsilon, \lambda\))-topology ⋮ Convergence in probability and almost surely convergence in probabilistic normed spaces ⋮ THE RANDOM SUBREFLEXIVITY OF COMPLETE RANDOM NORMED MODULES ⋮ Ekeland's variational principle for an \(\overline{L}^0\)-valued function on a complete random metric space ⋮ Lacunary ideal convergence of multiple sequences in probabilistic normed spaces ⋮ On almost surely bounded semigroups of random linear operators ⋮ The algebraic structure of finitely generated \(L^0(\mathcal F, K)\)-modules and the Helly theorem in random normed modules ⋮ Generalized ideal convergence in probabilistic normed spaces

Cites Work

• Multiplications on the space of probability distribution functions
• Probabilistic norms for linear operators
• On the definition of a probabilistic normed space
• Completion of probabilistic normed spaces
• A metric for weak convergence of distribution functions
• Entfernung zweier zufälliger Grössen und die Konvergenz nach Wahrscheinlichkeit
• Metrics and Norms on Spaces of Random Variables
• Remarks on the convergence of measurable sets and measurable functions
• A study of boundedness in probabilistic normed spaces
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