A pointwise ergodic theorem along return times of rapidly mixing systems
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3730-3748, December 2025.Abstract We introduce a new class of sparse sequences that are ergodic and pointwise universally L2$L^2$‐good for ergodic averages; that is, sequences along which the ergodic averages converge almost surely to the projection to invariant functions.
Sebastián Donoso +2 more
wiley +1 more source
On the law of the iterated logarithm for the discrepancy of lacunary sequences [PDF]
Transactions of the American Mathematical Society, 2010 A classical result of Philipp (1975) states that for any sequence ( n k
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Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces
Abstract and Applied Analysis, 2013 We define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them.
S. A. Mohiuddine +2 more
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The Role of Lacunary Statistical Convergence for Double sequences in Neutrosophic Normed Spaces [PDF]
Neutrosophic Sets and SystemsThis paper introduces and explores the concept of lacunary statistical convergence of double sequence within the framework neutrosophic normed spaces. Neutrosophic normed spaces extend classical normed spaces by incorporating neutrosophic numbers, which ...
Jenifer. P, Jeyaraman. M
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Discatenated and lacunary recurrences [PDF]
Notes on Number Theory and Discrete MathematicsRecursive sequences with gaps have been studied previously. This paper considers some elementary properties of such sequences where the gaps have been created on a regular basis from sequence to sequence – ‘discatenated’ (systematic gaps) and ‘lacunary’
Hakan Akkuş +3 more
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Some Geometric Properties of Sequence Spaces Involving Lacunary Sequence [PDF]
Journal of Inequalities and Applications, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Construction of Lacunary Sequence Spaces via Modulus Function and Nörlund-Mean of Order α
AxiomsIn this work, we introduce new classes of lacunary sequence spaces based on Nörlund-type means, a sequence of modulus functions and the order parameter ...
Hong-Wei Wang +4 more
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On Asymptotically Double Lacunary Statistical Equivalent Sequences in Probabilistic Normed Space
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012 In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.
Esi Ayhan
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Lacunary statistical summability of sequences of sets
, 2014 In this paper we define the WS_θ-analog of the Cauchy criterion for convergence and show that it is equivalent to Wijsman lacunary statistical convergence. Also, Wijsman lacunary statistical convergence is compared to other summability methods which are defined in this paper.
Ulusu, Uğur, Nuray, Fatih
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Riesz lacunary uniform integrability and statistical convergence via power series method
Journal of Inequalities and ApplicationsIn this paper, the concepts of Riesz lacunary statistical convergence, Riesz lacunary strong convergence, and Riesz lacunary uniform integrability of real sequences within the framework of power series are introduced and studied.
Jun-Jie Quan +3 more
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