K.J. Falconer and O.B. Springer, Order-two density of sets and measures with nonintegral dimension, Mathematika, 42(1995), 1-14. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Symmetry Properties of Average Densities and Tangent Measure.. - Mörters (1996) (1 citation) (Correct)
....example [5] 19] and [7] have extended this result to various other classes of fractal measures with self similarity properties. Average densities have also been used for the investigation of general measures with positive lower and nite upper densities. For example, Falconer and Springer in [6] and Marstrand in [11] generalize a classical inequality of Marstrand using average densities and in [16] it is shown that the lower one sided average densities do not vanish. In [4] Bedford and Fisher ask whether the left sided and right sided average densities always agree. An answer to this ....
K.J. Falconer and O.B. Springer, Order-two density of sets and measures with nonintegral dimension, Mathematika, 42(1995), 1-14.
On One-Sided Average Densities of Fractal Measures on the Line - Mörters, Preiss (1996) (Correct)
....and [PZ93] 1 have shown that for particular classes of fractal measures the lower and upper average densities agree. This also applies to the one sided average densities. But average densities can also be used for the investigation of more general measures. For example, Falconer and Springer in [FS95] generalize a classical inequality of Marstrand involving average densities. In this paper we show that for a measure with bounded densities the one sided average densities are bounded away from 0. More precisely: Theorem Suppose is a Radon measure on the real line such that for some 0 c C ....
K.J. Falconer and O.B. Springer. Order-two density of sets and measures with non-integral dimension. Mathematika, 42:1-14, 1995.
Average Densities, Tangent Measures and Rectifiability - Mörters (Correct)
....expect to infer regularity of from the equality of the lower and upper average densities, but it is interesting to ask for the consequences of equality of the lower and lower average densities or of the upper and upper average densities. This problem was first studied by Falconer and Springer in [FS95] and their results were recently improved by Marstrand in [Mar96] They showed the following theorem: Theorem 2.1 Suppose is a nonnegative, nonzero Radon measure on IR d and ff 0 such that (i) 0 D ff ( x) d ff ( x) 1 for almost every x, or (ii) 0 d ff ( x) D ff ( x) ....
K.J. Falconer and O.B. Springer, Order-two density of sets and measures with non-integral dimension, Mathematika, 42:1--14, 1995.
Small scale limit theorems for the intersection local times.. - Mörters, Shieh (1999) (Correct)
.... (r) r ff . Examples include Hausdoroe measures on deterministic and random selfsimilar sets, mixing repellers or occupation measures of stable processes, see [BF92] PZ94] KF92] and [FX95] We remark that average densities were also used to characterize geometric regularity of sets, see [FS95], JM96] PM97] or symmetry properties of measures, see [M98a] MP98] Our rst result shows that for the intersection local time measure on the intersection of two Brownian paths in 3 space an average density of order two may be de ned using such a gauge function. Theorem 1.1 Suppose is ....
K.J. Falconer and O.B. Springer. Ordertwo density of sets and measures with nonintegral dimension. Mathematika. 42 (1995) 114.
Tangent Measure Distributions of Fractal Measures - Mörters, Preiss (1996) (Correct)
....Consequently, the local geometry of general measures is not different from the local geometry of self similar sets. The strength of this result is illustrated by pointing out how it can be used to improve or generalize recently proved relations between ordinary and average densities (e.g. [FaSp], Ma2] or [Mo2] Mathematics Subject Classification (1995) 28A80, 28A75, 60G57. 1. The result and its background The study of the regularity of the local behaviour of a measure on a Euclidean space is much simplified by the fact that, under the presence of mild a priori estimates, the weak ....
.... the measure has, in reality, dimension smaller than ff) We believe that this result reveals a wealth of new unexpected information about the structure of such general measures, and we illustrate this by giving several examples of its application to questions studied previously in [MoPr] Mo2] [FaSp] and [Ma2] We should also remark that our result is new already on the line. However, in the important case of measures on the line with positive lower and finite upper Tangent measure distributions of fractal measures 3 densities it is possible to deduce the Palm property of tangent measure ....
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K.J. Falconer and O.B. Springer. Order--two density of sets and measures with non-- integral dimension. Mathematika, 42:1--14, 1995.
Average Densities And Linear Rectifiability Of Measures - Mörters (Correct)
....the following inequalities: d ff ( x) D ff ( x) D ff ( x) d ff ( x) It is natural to ask whether one can get statements about the geometric regularity of from weaker inequalities than (1) involving the average densities. This program was started by Falconer and Springer in [FS95] and their results were recently improved by Marstrand (see [Mar96] who proved the following theorem: Theorem 1.1 Suppose is a nonnegative, nonzero Radon measure on IR d and ff 0 such that (i) 0 D ff ( x) d ff ( x) 1 for almost every x, or (ii) 0 d ff ( x) D ff ....
K.J. Falconer and O.B. Springer, Order-two density of sets and measures with non-integral dimension, Mathematika, 42:1--14, 1995.
Symmetry Properties of Average Densities and Tangent Measure.. - Mörters (Correct)
No context found.
K.J. Falconer and O.B. Springer, Order-two density of sets and measures with nonintegral dimension, Mathematika, 42(1995), 1-14.
Average Densities and Linear Rectifiability of Measures - Mörters (Correct)
No context found.
K.J. Falconer and O.B. Springer, Order-two density of sets and measures with non-integral dimension, Mathematika, 42:1--14, 1995. 11
Average Densities, Tangent Measures and Rectifiability - Mörters (Correct)
No context found.
K.J. Falconer and O.B. Springer, Order-two density of sets and measures with non-integral dimension, Mathematika, 42:1--14, 1995.
On One-Sided Average Densities of Fractal Measures on the Line - Mörters, Preiss (Correct)
No context found.
K.J. Falconer and O.B. Springer. Order-two density of sets and measures with non-integral dimension. Mathematika, 42:1-14, 1995.
The Average Density of the Path of Planar Brownian Motion - Mörters (Correct)
No context found.
K.J. Falconer and O.B. Springer. Order--two density of sets and measures with non--integral dimension. Mathematika. 42 (1995) 1--14.
Average Densities and Linear Rectifiability of Measures - Mörters (Correct)
No context found.
K.J. Falconer and O.B. Springer, Order-two density of sets and measures with non-integral dimension, Mathematika, 42:1--14, 1995. 11
The Average Density of the Path of Planar Brownian Motion - Mörters (Correct)
No context found.
K.J. Falconer and O.B. Springer. Order--two density of sets and measures with non--integral dimension. Mathematika. 42 (1995) 1--14.
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