On vector sums of measure zero sets.
Kharazishvili, A. (2001)
Georgian Mathematical Journal
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Kharazishvili, A. (2001)
Georgian Mathematical Journal
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Ryszard Rudnicki (1991)
Annales Polonici Mathematici
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We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.
Claude Laflamme (1992)
Colloquium Mathematicae
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David Fremlin (2000)
Fundamenta Mathematicae
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I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.
Ai Fan (1995)
Colloquium Mathematicae
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Let T be a d×d matrix with integer entries and with eigenvalues >1 in modulus. Let f be a lipschitzian function of positive order. We prove that the series converges almost everywhere with respect to Lebesgue measure provided that .
Yohann de Castro (2011)
Annales mathématiques Blaise Pascal
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In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown that, in the Gauss space, a set of given measure and almost minimal Gauss boundary measure is necessarily close to be a half-space. Using only geometric tools, we extend their result to all symmetric log-concave measures on the real line. We give sharp quantitative isoperimetric inequalities and prove that among sets of given measure and given asymmetry (distance to half line, i.e. distance to sets...
Yasushige Watase, Noboru Endou, Yasunari Shidama (2008)
Formalized Mathematics
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This article contains some definitions and properties refering to function spaces formed by partial functions defined over a measurable space. We formalized a function space, the so-called L1 space and proved that the space turns out to be a normed space. The formalization of a real function space was given in [16]. The set of all function forms additive group. Here addition is defined by point-wise addition of two functions. However it is not true for partial functions. The set of partial...
Haribash, Najemedin (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Bonciocat, N.C., Zaharescu, A. (2005)
Acta Mathematica Universitatis Comenianae. New Series
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Wojciech Bartoszek, Ryszard Rębowski (1996)
Colloquium Mathematicae
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