2015/07/04 by Gogi Pantsulaia, Pantsulaia, Gogi, Tengiz Kiria +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #03xx #28C10 #28xx #Classical Analysis and ODEs (math.CA) #F.2.1 #FOS: Mathematics #Mathematical Approximation and Integration #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1507.02978
openalex publication_date 2015/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the proof of a certain modified version of Kolmogorov's strong law of large numbers for calculation of Lebesgue Integrals by using uniformly distributed sequences in (0,1). We extend the result of C. Baxa and J. Schoiβengeier (cf.\citeBaxSch2002, Theorem 1, p. 271) to a maximal set of uniformly distributed (in (0,1)) sequences Sf ⊂(0,1)∞ which strictly contains the set of sequences of the form (\αn\)_n ∈ \bf N with irrational number α and for which ℓ1∞(Sf)=1, where ℓ1∞ denotes the infinite power of the linear Lebesgue measure ℓ1 in (0,1).