Measure preserving transformations and rearrangements
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This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1970-08-01 and is currently open access. It has received 123 citations till now. The article focuses on the topics: Measure (physics).read more
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Book
A First Course in Sobolev Spaces
TL;DR: Leoni as discussed by the authors takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable.
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On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
TL;DR: In this paper, the authors considered the stochastic difference equation Y n = A n Y n-1 + B n with i.i.d. random pairs (A n, B n ) and obtained conditions under which Y n converges in distribution.
On a stochastic difference equation and a representation of non-negative
TL;DR: In this article, the stochastic difference equation Y, =AY_-1+B, with i.i.d. random pairs (An,B) was considered and conditions under which Y converges in distribution.
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A simple nonparametric estimator of a strictly monotone regression function
TL;DR: In this article, a new method for monotone estimation of a regression function is proposed, which is potentially attractive to users of conventional smoothing methods, and the main idea of the new approach is to construct a density estimate from the estimated values m(i/N) (i = 1,..., N) of the regression function and to use these 'data' for the calculation of an estimate of the inverse of the regressions.
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A Representation Result for Concave Schur Concave Functions
TL;DR: In this paper, it was shown that weakly upper semicontinuous concave Schur concave functions are the infinimum of nonnegative affine combinations of Choquet integrals with respect to a convex continuous distortion of the underlying probability.
References
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Theory Of The Integral
TL;DR: In this article, the integral in an abstract space is defined as the integral integral in the abstract space of the integral space of an abstract representation of a set of elements. But,
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On some singular monotonic functions which are strictly increasing
TL;DR: The existence of strictly increasing singular functions has been studied in the context of monotonic continuous functions, which are increasing in the strict sense, that is, f(x') >f(x) whenever x' >x.
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Differences, derivatives, and decreasing rearrangements
TL;DR: The decreasing rearrangement of a finite sequence a 1, a 2, … , an of real numbers is a second sequence a π(1), a ρ(2), …, aπ(n) , where π (l), τ(2) is a permutation of 1,2, …, n and (1, p. 260).