Last Updated：2025/12/06
Sentence
外測度は、全ての部分集合に定義された前測度から導かれる測度類似の関数であり、任意の集合に対してその集合を被覆する前測度可能な集合族の前測度の下限を与え、空集合に対して0を与え、単調性と可算部分加法性を満たす。
Quizzes for review
The outer measure assigns to each subset the infimum of the premeasures of all countable covers by premeasurable sets, ensuring monotonicity, subadditivity, and that the empty set has measure zero.
See correct answer
The outer measure assigns to each subset the infimum of the premeasures of all countable covers by premeasurable sets, ensuring monotonicity, subadditivity, and that the empty set has measure zero.
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Related words
outer measure
Noun
(mathematical
analysis,
measure
theory)
A
measure-like
function
derived
from
some
premeasure
as
follows:
when
it
is
applied
to
a
set
E,
it
yields
the
infimum
of
the
premeasures
of
all
possible
premeasurable
covers
of
E.
More
abstractly,
a
measure-like
function
whose
domain
is
the
power
set
of
some
underlying
set,
which
has
the
properties
of
(1)
yielding
zero
when
applied
to
the
empty
set,
(2)
being
monotonic
(if
A
is
subset
of
B
then
this
function
applied
to
A
is
less-than-or-equal
to
this
function
applied
to
B),
(3)
being
subadditive
(if
A
is
a
countable
sum
of
Bⱼ's
then
this
function
applied
to
A
is
less-than-or-equal
to
the
sum
of
the
applications
of
this
function
to
the
Bⱼ's).
Japanese Meaning
外側測度: 測度論において、あるプリアィメジャーから派生して定義される関数で、ある集合に対して、その集合を覆うすべてのプリアィメジャ可能な被覆のプリアィメジャーの下限を取るもの。 / 性質として、空集合に対してゼロを与え、単調性（ある集合が別の集合の部分集合なら、その外側測度もそれに対応して小さいか等しくなる）や、可算部分加法性（無限個の集合の和集合に対して、その外側測度は各集合の外側測度の和以上にならない）を満たす。
Related Words
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