Last Updated：2025/11/26
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In Euclidean space, the Lebesgue measure is the unique complete translation-invariant measure on the σ-algebra containing all k-cells that assigns to each k-cell its Euclidean volume.
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In Euclidean space, the Lebesgue measure is the unique complete translation-invariant measure on the σ-algebra containing all k-cells that assigns to each k-cell its Euclidean volume.
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Related words
Lebesgue measure
IPA(Pronunciation)
Noun
(mathematical
analysis)
A
unique
complete
translation-invariant
measure
for
the
σ-algebra
which
contains
all
k-cells
in
a
given
Euclidean
space,
and
which
assigns
a
measure
to
each
k-cell
which
is
equal
to
that
k-cell's
volume
(as
defined
in
Euclidean
geometry:
i.e.,
the
volume
of
the
k-cell
equals
the
product
of
the
lengths
of
its
sides).
Japanese Meaning
与えられたユークリッド空間内のk-セルすべてを含むσ‐代数上で定義される、一意的で完全な平行移動不変な測度。各k-セルに対して、そのユークリッド幾何学に基づく体積（すなわち、各辺の長さの積として定義される量）を割り当てる。
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