最終更新日：2024/07/31
(mathematical analysis) A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero.
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Hausdorff dimension
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元となった辞書の項目
Hausdorff dimension
noun
(mathematical
analysis)
A
type
of
fractal
dimension,
a
real-valued
measure
of
a
geometric
object
that
assigns
1
to
a
line
segment,
2
to
a
square
and
3
to
a
cube.
Formally,
given
a
metric
space
X
and
a
subset
of
X
labeled
S,
the
Hausdorff
dimension
of
S
is
the
infimum
of
all
real-valued
d
for
which
the
d-dimensional
Hausdorff
content
of
S
is
zero.
意味（1）
(mathematical
analysis)
A
type
of
fractal
dimension,
a
real-valued
measure
of
a
geometric
object
that
assigns
1
to
a
line
segment,
2
to
a
square
and
3
to
a
cube.
Formally,
given
a
metric
space
X
and
a
subset
of
X
labeled
S,
the
Hausdorff
dimension
of
S
is
the
infimum
of
all
real-valued
d
for
which
the
d-dimensional
Hausdorff
content
of
S
is
zero.
