Calculation of Lebesgue integrals by using uniformly distributed sequences
A certain modified version of Kolmogorov’s strong law of large numbers is used for an extension of the result of C. Baxa and J. Schoißengeier (2002) to a maximal set of uniformly distributed sequences in (0,1) which strictly contains the set of all sequences having the form ({αn})n∈N for some irrati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-12-01
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| Series: | Transactions of A. Razmadze Mathematical Institute |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2346809216300034 |
| Summary: | A certain modified version of Kolmogorov’s strong law of large numbers is used for an extension of the result of C. Baxa and J. Schoißengeier (2002) to a maximal set of uniformly distributed sequences in (0,1) which strictly contains the set of all sequences having the form ({αn})n∈N for some irrational number α and having the full ℓ1∞-measure, where ℓ1∞ denotes the infinite power of the linear Lebesgue measure ℓ1 in (0,1). Keywords: Uniformly distributed sequence, Lebesgue integral, Strong law of large numbers |
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| ISSN: | 2346-8092 |