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SOME REMARKS ON GENERALIZED BOREL MEASURES IN TOPOLOGICAL SPACES
"... Given a set A, we shall denote by IAI the cardinality of A and by exp A the family of all subsets of A. Through~ out, a will denote an uncountabZe cardinal and S, y, will denote infinite cardinals. Whenever convenient, we shall identify a cardinal with its initial ordinal. As usual, we shall denote ..."
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mbe an aalgebra in a set M. A function ~: m ~ [0,+00] is called an ameasupe on m if ~(~) = 0 and v(UA) = L{~(A): A E A} for each disjoint family A c /i) with IAI < a. The triple (M,m,~) is called an ameasure space. Definition 3. Let (M,m,V) be an ameasure space. The ameasure V is called S
BOREL MEASURES WITH A DENSITY ON A COMPACT SEMIALGEBRAIC SET
, 2013
"... Abstract. Let K ⊂ R n be a compact basic semialgebraic set. We provide a necessary and sufficient condition (with no à priori bounding parameter) for a real sequence y = (yα), α ∈ N n, to have a finite representing Borel measure absolutely continuous w.r.t. the Lebesgue measure on K, and with a den ..."
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Abstract. Let K ⊂ R n be a compact basic semialgebraic set. We provide a necessary and sufficient condition (with no à priori bounding parameter) for a real sequence y = (yα), α ∈ N n, to have a finite representing Borel measure absolutely continuous w.r.t. the Lebesgue measure on K, and with a
Invariant finite Borel measures for rational functions on the Riemann sphere
"... To study finite Borel measures on the Riemann sphere invariant under a rational function R of degree greater than one, we decompose them in an Rinvariant component measure supported on the Julia set and a finite number of mutually singular Rinvariant component measures vanishing on the Julia set. ..."
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To study finite Borel measures on the Riemann sphere invariant under a rational function R of degree greater than one, we decompose them in an Rinvariant component measure supported on the Julia set and a finite number of mutually singular Rinvariant component measures vanishing on the Julia set
On the difference property of Borel measurable functions Hiroshi Fujita (Matsuyama)
, 2008
"... If an atomlessly measurable cardinal exists, then the class of Lebesgue measurable functions, the class of Borel functions, and the Baire classes of all order have the difference property. This gives a consistent positive answer to Laczkovich’s Problem 2 posed in [11]. We also give a complete positi ..."
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If an atomlessly measurable cardinal exists, then the class of Lebesgue measurable functions, the class of Borel functions, and the Baire classes of all order have the difference property. This gives a consistent positive answer to Laczkovich’s Problem 2 posed in [11]. We also give a complete
TYPICAL BOREL MEASURES ON [0, 1] d SATISFY A MULTIFRACTAL FORMALISM
"... Abstract. In this article, we prove that in the Baire category sense, measures supported by the unit cube of R d typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifractal spectrum of such typical measures µ. This spectrum appears to be linear with slope 1, s ..."
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Cited by 1 (1 self)
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Abstract. In this article, we prove that in the Baire category sense, measures supported by the unit cube of R d typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifractal spectrum of such typical measures µ. This spectrum appears to be linear with slope 1
Borel measures of polynomial growth and classical convolution inequalities, (in preparation
, 2014
"... ar ..."
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1330 (24 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 766 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a preliminary theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled d...
Results 11  20
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59,297