Lebesgue measure
Lebesgue Measure of Generalized Cantor Set
... Random measure [12]. In this paper, we discuss the construction and some properties of generalized Cantor set. We show that this special type of set is measurable set, Borel set as well as Borel measurable whose ...
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An infinitely generated self similar set with positive Lebesgue measure and empty interior
... positive Lebesgue measure and empty interior? This question was answered in the affirmative by Cs¨ ornyei et al in ...positive Lebesgue measure and empty ...
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Multiple Lebesgue integration on time scales
... a Lebesgue measure in an ab- stract setting is ...the Lebesgue multi-dimensional delta measure on time scales is introduced and the Lebesgue delta measure of any single-point set ...
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Measurable circle squaring
... non-zero Lebesgue measure and the upper box dimension of the boundary of each set is less than k, then there is a partition of A into finitely many parts that can be translated to form a partition of ...
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Metrical Diophantine approximation for quaternions
... the Lebesgue measure of a set E will be denoted by ...Hausdorff measure and Hausdorff dimension are much more general and can be assigned to any ...
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Improvements of the Hermite Hadamard inequality for the simplex
... Lemma . is an extension of the Fejér inequality (see []) to multivariable convex func- tions. As regards univariable convex functions, using the Lebesgue measure on R and a closed interval as -simplex ...
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Equidistribution for nonuniformly expanding dynamical systems, and application to the almost sure invariance principle
... For example, if M = [0, 1] and T is a nonuniformly expanding map as in Young [23] such as intermittent or logistic with a Collet-Eckmann parameter, then µ may be (a) the Lebesgue measure, (b) the absolutely ...
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Beta-expansions, natural extensions and multiple tilings associated with pisot untis
... the Lebesgue measure; under certain con- ditions, they provide Markov partitions of the torus; they characterize the numbers with purely periodic expansion, and they allow determining any digit in an ...
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Some Features for Blow-up Solutions of a Nonlinear Parabolic Equation
... The following theorem follows Theorem 10 and is an important property for regions in which solutions blow up with the same rate as the maximum points.. has positive Lebesgue measure.[r] ...
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Torsional rigidity for regions with a Brownian boundary
... Abstract Let T m be the m-dimensional unit torus, m ∈ N . The torsional rigidity of an open set ⊂ T m is the integral with respect to Lebesgue measure over all starting points x ∈ of the expected lifetime ...
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An analogue of Khintchine's theorem for self conformal sets
... Khintchine’s theorem is a classical result from metric number theory which relates the Lebesgue measure of certain limsup sets with the convergence/divergence of naturally occurring volume sums. In this ...
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A Study of the Lhires III Spectrograph on the Hard Labor Creek Observatory 20 inch Telescope
... We look from a new point of view at the denition and basic properties of the Lebesgue measure and integral on Euclidean spaces, on abstract spaces, and on locally compact Haus- dor spaces. We use mini sums ...
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Differentiability of Lipschitz functions in Lebesgue null sets
... We now estimate the average integral of each of the terms on the right side. Most of the estimates are very similar to those in [16]. The main difference is in the estimate of the regularity term. Here we need to account ...
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Analysis of Lebesgue Integral Functions and Theorems
... The Lebesgue integral provides the right abstractions needed to do this important ...term Lebesgue integration can mean either the general theory of integration of a function with respect to a general ...
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On an integral operator on the unit ball in
... A natural question is to define a similar integral operator which acts on HB the space of all holomorphic functions in the unit ball B.. Let dVN stand for the normalized Lebesgue measure[r] ...
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Badly approximable points in twisted Diophantine approximation and Hausdorff dimension
... Lebesgue measure zero, and Schmidt proved in 1966 that the particular set Bad(1/2, 1/2) has full Hausdorff dimension. But the result of maximal dimension in the weigthed setting hasn’t been proved until ...
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The Dominating Set of Bergman Spaces
... Proof of Main Theorem We can now characterize a special family of reverse Carleson measures for weighted Bergman spaces with the weighted Lebesgue measure.. The main results is as follow[r] ...
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Statistical Inference for a New Class of Multivariate Pareto Distributions
... dominating measure, instead of the Lebesgue measure, which makes the MLE method feasible, and we discuss the expectation maximization (EM) algorithm to estimate the parameters in Section ...
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Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes
... Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the projection onto any line with direction outside X, of any subset F of E of positive s-dimensional ...
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On Young Functionals Related to Certain Class of Rapidly Oscillating Sequences
... Young measure as at object asso- ciated with any measurable function defined on a nonempty, open, bounded subset Ω of R d with values in a compact subset K of R l ...Young measure associated with a simple ...
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