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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On the geometry of convex sets.

100%
Moszyńska M.
Mathematica Applicanda
|
2004
|
tom 32
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nr 46/05
EN
.
2
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Various categorical approaches to statistical spaces

69%
Bromek T., Moszyńska M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction..............................................................................................................5 1. Preliminaries........................................................................................................6 1.0. Measurable, probabilistic, and statistical spaces..............................................6 1.1. Transition functions..........................................................................................6 1.2. Linear space of P-bounded measurable real functions....................................8 1.3. Almost transition functions................................................................................9 2. Concrete categories of measurable, probabilistic, and statistical spaces..........14 3. Categories connected with transition functions..................................................16 3.1. Category $Mes_{trans}$.................................................................................16 3.2. Category $St_{trans}$....................................................................................19 3.3. Category $St_{dist}$......................................................................................20 3.4. Categories of indexed statistical spaces.........................................................23 4. Categories connected with almost transition functions......................................23 Final remarks.........................................................................................................27 References............................................................................................................28
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Concerning Sets of the First Baire Category with Respect to Different Metrics

64%
Moszyńska M., Sójka G.
Bulletin of the Polish Academy of Sciences. Mathematics
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2010
|
tom 58
|
nr 1
47-54
EN
We prove that if $ϱ_H$ and δ are the Hausdorff metric and the radial metric on the space 𝓢ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family 𝓐 ⊂ 𝓢ⁿ that is meager with respect to $ϱ_H$ need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in 𝓢ⁿ with respect to δ.
4
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On metric products

64%
Herburt I., Moszyńska M.
Colloquium Mathematicum
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1991
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tom 62
|
nr 1
121-133
5
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Optimal isometries for a pair of compact convex subsets of ℝⁿ

64%
Herburt I., Moszyńska M.
Banach Center Publications
|
2009
|
tom 84
|
nr 1
111-120
EN
In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for $L_p$ metrics for all p ≥ 2 and the symmetric difference metric.
6
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Fractal star bodies

51%
Herburt I., Moszyńska M., Pronk D.
Banach Center Publications
|
2009
|
tom 84
|
nr 1
149-171
EN
In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for $L_p$ metrics for all p ≥ 2 and the symmetric difference metric.
7
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On shape and fundamental deformation retracts

38%
Moszyńska M.
Fundamenta Mathematicae
|
1972
|
tom 75
|
nr 2
145-167
8
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On rigid subsets of some manifolds

32%
Moszyńska M.
Colloquium Mathematicum
|
1989
|
tom 57
|
nr 2
247-254
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