The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a smooth curve in the plane, and area of a smooth surface in space, to arbitrary measurable sets. It is typically applied to fractal boundaries of domains in the Euclidean space, but it can also be used in the context of general metric measure spaces. It is related to, although different from, the Hausdorff measure.
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| - Minkowski content (en)
- Ёмкость Минковского (ru)
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| - The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a smooth curve in the plane, and area of a smooth surface in space, to arbitrary measurable sets. It is typically applied to fractal boundaries of domains in the Euclidean space, but it can also be used in the context of general metric measure spaces. It is related to, although different from, the Hausdorff measure. (en)
- Ёмкость Минковского — основное понятие в геометрической теории меры, обобщающее на произвольные измеримые множества понятиядлины кривой на плоскости иплощади поверхности в пространстве. Ёмкость обычно применяется для фрактальных границ областей в евклидовом пространстве, но имеет смысл в контексте общих метрических пространств с мерой. Названа в честь Германа Минковского. (ru)
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| - The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a smooth curve in the plane, and area of a smooth surface in space, to arbitrary measurable sets. It is typically applied to fractal boundaries of domains in the Euclidean space, but it can also be used in the context of general metric measure spaces. It is related to, although different from, the Hausdorff measure. (en)
- Ёмкость Минковского — основное понятие в геометрической теории меры, обобщающее на произвольные измеримые множества понятиядлины кривой на плоскости иплощади поверхности в пространстве. Ёмкость обычно применяется для фрактальных границ областей в евклидовом пространстве, но имеет смысл в контексте общих метрических пространств с мерой. Названа в честь Германа Минковского. (ru)
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