Some Limit Theorems for Random Functions. I

1959/01/01 by V. A. Volkonskii, В. А. Волконский, Yu. A. Rozanov · 5 citations
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Functional Equations Stability Results

paper · doi:10.1137/1104015

crossref issued 1959/01/01 · crossref published 1959/01/01 · crossref published-print 1959/01/01 · openalex publication_date 1959/01/01 · crossref created 2005/03/07 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/01

Abstract

This paper establishes a number of limit theorems for random functions H(Δ ) in the interval Δ , which satisfy the “strong mixing condition” \mathop lim _{τ → ∞} \mathop sup _t \mathop sup _A ∈ M_∞ ^t ,B ∈ M_{t + τ} ^∞ | \bf P(AB) - \bf P(A)\bf P(B) | = 0 where \mathfrakM_t1 ^t₂ is a σ -algebra generated by events \ H(Δ ₁ ) < h₁ , ⋯ ,H(Δ _n ) < h_n \ ,Δ ₁ , ⋯ ,Δ _n are arbitrary intervals, Δ _k ⊆ (t₁ ,t₂ ),h₁ , ⋯ h_n are arbitrary real numbers.

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