-continuous multivalued maps
J. Eweret (1989)
Matematički Vesnik
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J. Eweret (1989)
Matematički Vesnik
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Roland Zweimüller (2002)
Colloquium Mathematicae
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We construct maps T on the interval and on the circle which are Lebesgue exact preserving an absolutely continuous infinite measure μ ≪ λ, such that for any probability measure ν ≪ λ the sequence of arithmetical averages of image measures does not converge weakly.
Anders Johansson, Anders Öberg, Mark Pollicott (2012)
Journal of the European Mathematical Society
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We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the -measure.
Regina Cohen, James W. Fickett (1982)
Colloquium Mathematicae
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Yu Deng (2015)
Journal of the European Mathematical Society
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In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than , extending the well-posedness result of Molinet [20].
Gogi Pantsulaia (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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New concepts of Lebesgue measure on are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on for α = (1,1,...).
Abdessatar Barhoumi, Habib Ouerdiane, Anis Riahi (2007)
Banach Center Publications
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he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure , via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure by using the so-called β-type Wick product.
Mrinal Kanti Roychowdhury (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension of ν and bounded above by a unique number , related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.
Ryotaro Sato (2004)
Colloquium Mathematicae
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Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and in measure for some f ∈ M(μ;X), then also in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X)...
S. Moll (2008)
Banach Center Publications
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Let X be a completely regular Hausdorff topological space and the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of .
Jesús Bastero, Julio Bernués (2009)
Studia Mathematica
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We study the asymptotic behaviour, as n → ∞, of the Lebesgue measure of the set for a random k-dimensional subspace E ⊂ ℝⁿ and an isotropic convex body K ⊂ ℝⁿ. For k growing slowly to infinity, we prove it to be close to the suitably normalised Gaussian measure in of a t-dilate of the Euclidean unit ball. Some of the results hold for a wider class of probabilities on ℝⁿ.
S. Lasher (1968)
Studia Mathematica
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G. Pantsulaia (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift of μ by a vector are neither equivalent nor orthogonal. This extends a result established in [7].
Alberto Bressan, Agostino Cortesi (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si dimostra che ogni funzione multivoca lipschitziana con costante di Lipschitz , definita su un sottoinsieme di uno spazio di Hilbert a valori compatti e convessi in , può essere estesa su tutto ad una funzione multivoca lipschitziana con costante minore di 7 nM. In generale, non esistono invece estensioni aventi la stessa costante di Lipschitz .
Andrzej Kisielewicz (1996)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has . Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
Piotr Niemiec (2009)
Studia Mathematica
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It is proved (independently of the result of Holmes [Fund. Math. 140 (1992)]) that the dual space of the uniform closure of the linear span of the maps x ↦ d(x,a) - d(x,b), where d is the metric of the Urysohn space of diameter r, is (isometrically if r = +∞) isomorphic to the space of equivalence classes of all real-valued Lipschitz maps on . The space of all signed (real-valued) Borel measures on is isometrically embedded in the dual space of and it is shown that the image...
Eric Amar (2008)
Annales Polonici Mathematici
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Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual...
Charles E. C Cleaver (1973)
Colloquium Mathematicae
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Tom Kempton (2016)
Journal of the European Mathematical Society
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We study natural measures on sets of -expansions and on slices through self similar sets. In the setting of -expansions, these allow us to better understand the measure of maximal entropy for the random -transformation and to reinterpret a result of Lindenstrauss, Peres and Schlag in terms of equidistribution. Each of these applications is relevant to the study of Bernoulli convolutions. In the fractal setting this allows us to understand how to disintegrate Hausdorff measure by slicing,...
Márton Elekes, Juris Steprāns (2004)
Fundamenta Mathematicae
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We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from ) that less than many translates of a compact set of measure zero can cover ℝ.
Artur Avila, Mikhail Lyubich, Weixiao Shen (2011)
Journal of the European Mathematical Society
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We study the parameter space of unicritical polynomials . For complex parameters, we prove that for Lebesgue almost every , the map is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every , the map is either hyperbolic, or Collet–Eckmann, or infinitely renormalizable. These results are based on controlling the spacing between consecutive elements in the “principal nest” of parapuzzle pieces.
Uffe Haagerup, Hanne Schultz (2009)
Publications Mathématiques de l'IHÉS
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Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace affiliated with ℳ, such that the Brown measure of is concentrated...
Marek Beśka (2010)
Applicationes Mathematicae
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Let be a Gaussian sequence with for each i and suppose its correlation matrix is the matrix of some linear operator R:l₂→ l₂. Then for , i=1,2,..., where μ is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals , i=1,2,... .
Ross Stokke (2022)
Commentationes Mathematicae Universitatis Carolinae
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We show how the measure theory of regular compacted-Borel measures defined on the -ring of compacted-Borel subsets of a weighted locally compact group provides a compatible framework for defining the corresponding Beurling measure algebra , thus filling a gap in the literature.
Geraldo Botelho, Daniel Cariello, Vinícius V. Fávaro, Daniel Pellegrino, Juan B. Seoane-Sepúlveda (2013)
Studia Mathematica
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Stanisaw Szufla (1998)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We present a new theorem on the differential inequality . Next, we apply this result to obtain existence theorems for the equation .
Steeve Burnet, Alain Pietrus (2011)
Applicationes Mathematicae
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This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from to the closed subsets of . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.