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Non-differentiability of Feynman paths
A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and...
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Correction to: Quantitative Approximation by Nonlinear Picard–Choquet, Gauss–Weierstrass–Choquet and Poisson–Cauchy–Choquet Singular Integrals
Corrigendum to Results Math. (73)(2018), no. 3, Art. 92, 23 pp. Concerning the examples in Remark 4.3 and Remark 5.4, I correct a few calculations,...
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On a Weak Type Estimate for Sparse Operators of Strong Type
We define sparse operators of strong type on abstract measure spaces with ball-bases. Weak and strong type inequalities for such operators are proved.
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Non-absolutely Convergent Generalized Laplacian
For possibly discontinuous functions including, for instance, Sobolev functions, we present new Blaschke-Privaloff-type criteria for superharmonicity...
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On a Time and State Dependent Maximal Monotone Operator Coupled with a Swee** Process with Perturbations
In this paper, we state, in separable Hilbert spaces, the existence of absolutely continuous solutions for a couple of evolution problems governed by...
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Applications of the Theory of Orlicz Spaces to Vector Measures
Let (Ω, Σ, λ) be a finite complete measure space, ( E , ξ ) be a sequentially complete locally convex Hausdorff space and E ′ be its topological dual....
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A simplified construction of the Lebesgue integral
We present a modification of Riesz’s construction of the Lebesgue integral, leading directly to finite or infinite integrals, at the same time...
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Quantitative Approximation by Nonlinear Picard–Choquet, Gauss–Weierstrass–Choquet and Poisson–Cauchy–Choquet Singular Integrals
By using the concept of Choquet nonlinear integral with respect to a submodular set function, we introduce the nonlinear Picard–Choquet operators,...
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Boundary Representations of λ-Harmonic and Polyharmonic Functions on Trees
On a countable tree T , allowing vertices with infinite degree, we consider an arbitrary stochastic irreducible nearest neighbour transition operator P ...
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Uniform and Pointwise Quantitative Approximation by Kantorovich–Choquet Type Integral Operators with Respect to Monotone and Submodular Set Functions
In this paper, for the univariate Bernstein–Kantorovich, Szász–Mirakjan–Kantorovich and Baskakov–Kantorovich operators written in terms of the...
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Uniform nonintegrability of random variables
Recently, T. K. Chandra, T. -C. Hu and A. Rosalsky [Statist. Probab. Lett., 2016, 116: 27–37] introduced the notion of a sequence of random variables...
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On L p -integrability of a special double sine series formed by its blocks
In this paper we deal with a special double sine trigonometric series formed by its blocks. This type of trigonometric series is of particular...
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Generalizations of Hölder inequalities for Csiszar’s f-divergence
In this paper, we establish some new generalizations of the Hölder’s inequality involving Csiszar’s f -divergence of two probability measures. Some...
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Convex combinations, barycenters and convex functions
The article first shows one alternative definition of convexity in the discrete case. The correlation between barycenters, Jensen’s inequality and...
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A new proof of the monotone convergence theorem of Lebesgue integral on σ-class
In this short note a new proof of the monotone convergence theorem of Lebesgue integral on σ -class is given.