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dc.contributor.authorBaron, Karol-
dc.identifier.citationAequationes Mathematicae, Vol. 93, no. 2 (2019), s. 415-423pl_PL
dc.description.abstractGiven a probability space (Ω,A, P), a complete and separable metric space X with the σ-algebra B of all its Borel subsets and a B⊗A-measurable f : X ×Ω → X we consider its iterates fn defined on X × ΩN by f0(x, ω) = x and fn(x, ω) = f fn−1(x, ω), ωn for n ∈ N and provide a simple criterion for the existence of a probability Borel measure π on X such that for every x ∈ X and for every Lipschitz and bounded ψ : X → R the sequence 1 n n−1 k=0 ψ fk(x, ·) n∈N converges in probability to X ψ(y)π(dy).pl_PL
dc.rightsUznanie autorstwa 3.0 Polska*
dc.subjectRandom-valued functionspl_PL
dc.subjectWeak law of large numberspl_PL
dc.subjectConvergence in lawpl_PL
dc.subjectConvergence in probabilitypl_PL
dc.titleWeak law of large numbers for iterates of random-valued functionspl_PL
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