A.S. Besicovitch, On linear sets of points of fractional dimension, Math.Ann., 101(1929), 161-193. Home/Search Document Not in Database Summary Related Articles Check |
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Symmetry Properties of Average Densities and Tangent Measure.. - Mörters (1996) (1 citation) (Correct)
....have obvious self similarity properties. In [4] Bedford and Fisher introduce average or order two densities for the study of measures of fractional dimension. For these measures the density functions t 7 ( x t; x t] t uctuate as t tends to 0 and therefore the limit does not exist (see [3]) Bedford and Fisher apply a logarithmic average and de ne the lower and upper circular average densities as D ( x) lim inf 0 (j log j) 1 Z 1 ( x t; x t] t dt t ; 1 and D ( x) lim sup 0 (j log j) 1 Z 1 ( x t; x t] t dt t : The lower and ....
A.S. Besicovitch, On linear sets of points of fractional dimension, Math.Ann., 101(1929), 161-193.
On One-Sided Average Densities of Fractal Measures on the Line - Mörters, Preiss (1996) (Correct)
....One Sided Average Densities of Fractal Measures on the Line by Peter Morters and David Preiss By a theorem of A.S. Besicovitch (see [Bes29] or [Bes68]) the lower one sided ff densities d ff ( x) lim inf t 0 ( x; x t] t ff and d ff Gamma ( x) lim inf t 0 ( x Gamma t; x] t ff of a measure of fractional dimension ff on the real line vanish almost everywhere if the circular ff densities d ff ( x) lim sup t 0 ....
A.S. Besicovitch. On linear sets of points of fractional dimension (II). Journal of the London Mathematical Society, 43:548--550, 1968.
On One-Sided Average Densities of Fractal Measures on the Line - Mörters, Preiss (1996) (Correct)
....One Sided Average Densities of Fractal Measures on the Line by Peter Morters and David Preiss By a theorem of A.S. Besicovitch (see [Bes29] or [Bes68] the lower one sided ff densities d ff ( x) lim inf t 0 ( x; x t] t ff and d ff Gamma ( x) lim inf t 0 ( x Gamma t; x] t ff of a measure of fractional dimension ff on the real line vanish almost everywhere if the circular ff densities d ff ( x) lim ....
A.S. Besicovitch. On linear sets of points of fractional dimension. Mathematische Annalen, 101:161--193, 1929.
Operators with Singular Continuous Spectrum, IV.. - Rio, Jitomirskaya.. (1996) (10 citations) (Correct)
....ff 6= lim ffi#0 (x Gamma ffi; x ffi) ffi ff oe : 2.3) For ff = 0, W ff is empty; and for ff = 1, the theorem of de la Vall ee Poussin (see [30] or Theorem 7.15 of [29] says that (W 1 ) 0. For 0 ff 1, however, the situation is quite different: A result going back to Besicovitch [5] (also see Theorem 5.2 of [10] is that if is the restriction of h ff to a set of finite positive h ff measure, then is supported on W ff . Moreover, there are even examples of s where for a.e. x w.r.t. lim ffi#0 ln (x Gamma ffi; x ffi) ln(ffi) 1 and lim ffi#0 ln (x ....
.... Gamma q ln q (1 Gamma q) ln(1 Gamma q) ln 2 where q = Gamma2 ln 2 Gamma ln(1 Gamma p) ln p Gamma ln(1 Gamma p) As a final variant in this class of examples, we ll give an example of a measure supported by the set W ff defined in (2. 3) examples of this kind go back to Besicovitch [5]) Fix 0 p 1 p 2 1 2 . Define a measure d p1p2 on [0; 1] as follows: The variables a n (x) will be independent for different n but not identically distributed. Rather Prob(a n (x) 0) ae p 1 N n (N 1) N odd p 2 N n (N 1) N even: Then by the law of large numbers, one ....
Besicovitch, A.S.: On linear sets of points of fractional dimension. Math. Annalen 101, 161--193 (1929)
On One-Sided Average Densities of Fractal Measures on the Line - Mörters, Preiss Self-citation (Besicovitch) (Correct)
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A.S. Besicovitch. On linear sets of points of fractional dimension (II). Journal of the London Mathematical Society, 43:548--550, 1968.
On One-Sided Average Densities of Fractal Measures on the Line - Mörters, Preiss Self-citation (Besicovitch) (Correct)
No context found.
A.S. Besicovitch. On linear sets of points of fractional dimension. Mathematische Annalen, 101:161--193, 1929.
Symmetry Properties of Average Densities and Tangent Measure.. - Mörters (Correct)
No context found.
A.S. Besicovitch, On linear sets of points of fractional dimension, Math.Ann., 101(1929), 161-193.
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