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1

Equidecomposability of Jordan domains under groups of isometries

100%

Laczkovich M.

Fundamenta Mathematicae

|

2003

|

tom 177

|

nr 2

151-173

EN

Let $G_d$ denote the isometry group of $ℝ^d$. We prove that if G is a paradoxical subgroup of $G_d$ then there exist G-equidecomposable Jordan domains with piecewise smooth boundaries and having different volumes. On the other hand, we construct a system $ℱ_d$ of Jordan domains with differentiable boundaries and of the same volume such that $ℱ_d$ has the cardinality of the continuum, and for every amenable subgroup G of $G_d$, the elements of $ℱ_d$ are not G-equidecomposable; moreover, their interiors are not G-equidecomposable as geometric bodies. As a corollary, we obtain Jordan domains A,B ⊂ ℝ² with differentiable boundaries and of the same area such that A and B are not equidecomposable, and int A and int B are not equidecomposable as geometric bodies. This gives a partial solution to a problem of Jan Mycielski.

2

Measurability of functions with approximately continuous vertical sections and measurable horizontal sections

64%

Laczkovich M., Miller A. W.

Colloquium Mathematicum

|

1996

|

tom 69

|

nr 2

299-308

3

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A characterization of Jordan and Lebesgue measures

38%

Jakab Z., Laczkovich M.

Colloquium Mathematicum

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1978-1979

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tom 40

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nr 1

39-52

4

On Kemperman's inequality 2f(x)≤ f(x+h)+f(x+2h)

38%

Laczkovich M.

Colloquium Mathematicum

|

1984-1985

|

tom 49

|

nr 1

109-115

5

On the transformers of derivatives

32%

Laczkovich M., Petruska G.

Fundamenta Mathematicae

|

1978

|

tom 100

|

nr 3

179-199

6

Von Neumann's paradox with translations

32%

Laczkovich M.

Fundamenta Mathematicae

|

1988

|

tom 131

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nr 1

1-12

Ograniczanie wyników

3 Colloquium Mathematicum

3 Fundamenta Mathematicae

6 Laczkovich M.

1 Jakab Z.

1 Miller A. W.

1 Petruska G.

1 2003

1 1996

1 1988

1 1984

2 1978

Equidecomposability of Jordan domains under groups of isometries

Measurability of functions with approximately continuous vertical sections and measurable horizontal sections

A characterization of Jordan and Lebesgue measures

On Kemperman's inequality 2f(x)≤ f(x+h)+f(x+2h)

On the transformers of derivatives

Von Neumann's paradox with translations