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Probabilities and Lebesgue measure
"... In this paper we give some applications of Lebesgue measure and we will also estimate an integral from probability theory. 2000 Mathematical Subject Classification: 28A25 1. Lebesgue measure is frequent used in problems of the probability theory, in physics and other domains. It is sufficiently to r ..."
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In this paper we give some applications of Lebesgue measure and we will also estimate an integral from probability theory. 2000 Mathematical Subject Classification: 28A25 1. Lebesgue measure is frequent used in problems of the probability theory, in physics and other domains. It is sufficiently
B Lebesgue Measure and Integral
"... In this volume, measures make an appearance in essentially two distinct ways. First, Lebesgue measure on R (and sometimes on R 2 or R d), is used throughout to define the Fourier transform and the spaces that it acts upon, such as the Lebesgue spaces L p (R). Second, the class Mb(R) of bounded Borel ..."
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In this volume, measures make an appearance in essentially two distinct ways. First, Lebesgue measure on R (and sometimes on R 2 or R d), is used throughout to define the Fourier transform and the spaces that it acts upon, such as the Lebesgue spaces L p (R). Second, the class Mb(R) of bounded
RANDOMNESS – BEYOND LEBESGUE MEASURE
"... Much of the recent research on algorithmic randomness has focused on randomness for Lebesgue measure. While, from a computability theoretic point of view, the picture remains unchanged if one passes to arbitrary computable measures, interesting phenomena occur if one studies the the set of reals wh ..."
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Cited by 2 (1 self)
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Much of the recent research on algorithmic randomness has focused on randomness for Lebesgue measure. While, from a computability theoretic point of view, the picture remains unchanged if one passes to arbitrary computable measures, interesting phenomena occur if one studies the the set of reals
The OneDimensional Lebesgue Measure
"... Summary. The paper is the crowning of a series of articles written in the Mizar language, being a formalization of notions needed for the description of the onedimensional Lebesgue measure. The formalization of the notion as classical as the Lebesgue measure determines the powers of the PC Mizar sy ..."
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Summary. The paper is the crowning of a series of articles written in the Mizar language, being a formalization of notions needed for the description of the onedimensional Lebesgue measure. The formalization of the notion as classical as the Lebesgue measure determines the powers of the PC Mizar
on Full Lebesgue Measure Sets ∗
, 2004
"... We consider the nonparametric estimation of a function that is observed in white noise after convolution with a boxcar, the indicator of an interval (−a, a). In a recent paper Johnstone et al. (2004) have developped a wavelet deconvolution algorithm (called WaveD) that can be used for “certain ” box ..."
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” boxcar kernels. For example, WaveD can be tuned to achieve near optimal rates over Besov spaces when a is a Badly Approximable (BA) irrational number. While the set of all BA’s contains quadratic irrationals e.g. a = √ 5 it has Lebesgue measure zero, however. In this paper we derive two tuning scenarios
AN INEQUALITY FOR THE LEBESGUE MEASURE AND ITS APPLICATIONS
"... 85–86], the first author of this paper proved a new inequality for the Lebesgue measure and gave some applications. Here, we present a new applications of this inequality. 1. ..."
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85–86], the first author of this paper proved a new inequality for the Lebesgue measure and gave some applications. Here, we present a new applications of this inequality. 1.
Lebesgue measure. Denote
, 2002
"... Abstract. An equivalence between the GurovReshetnyak GR(ε) and Muckenhoupt A ∞ conditions is established. Our proof is extremely simple and works for arbitrary absolutely continuous measures. Throughout the paper, µ will be a positive measure on Rn absolutely continuous with respect to ..."
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Abstract. An equivalence between the GurovReshetnyak GR(ε) and Muckenhoupt A ∞ conditions is established. Our proof is extremely simple and works for arbitrary absolutely continuous measures. Throughout the paper, µ will be a positive measure on Rn absolutely continuous with respect to
On the Lebesgue Measure of SelfAffine Sets
 TURK J MATH
, 2001
"... Flaherty and Wang studied Haartype multiwavelets and multitiles. The information on what digit sets give multiattractors with positive Lebesgue measure is very limited. In this note, we give a few classes of digit sets leading to multiattractors with positive measure. The attractors we obtain i ..."
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Cited by 1 (0 self)
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Flaherty and Wang studied Haartype multiwavelets and multitiles. The information on what digit sets give multiattractors with positive Lebesgue measure is very limited. In this note, we give a few classes of digit sets leading to multiattractors with positive measure. The attractors we obtain
Bounded Archiving using the Lebesgue Measure
, 2003
"... Many modern multiobjective evolutionary algorithms (MOEAs) store the points discovered during optimization in an external archive, separate from the main population, as a source of innovation and/or for presentation at the end of a run. Maintaining a bound on the size of the archive may be desirable ..."
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Cited by 25 (1 self)
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by the archive. The new archiver is shown to outperform existing methods, on several problem instances, with respect to the quality of the archive obtained when judged using three distinct quality measures.
The Equivalence Of Some Bernoulli Convolutions To Lebesgue Measure
, 1998
"... Since the 1930’s many authors have studied the distribution νλ of the random series Yλ = ∑ ±λn where the signs are chosen independently with probability (1/2, 1/2) and 0 <λ<1. Solomyak recently proved that for almost every λ ∈ [ 1 2, 1], the distribution νλ is absolutely continuous with re ..."
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Cited by 24 (0 self)
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with respect to Lebesgue measure. In this paper we prove that νλ is even equivalent to Lebesgue measure for almost all λ ∈ [1/2, 1].
Results 1  10
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