Last Updated
：2025/11/26
Lebesgue integral
IPA(Pronunciation)
Noun
countable
definite
singular
singular-only
(mathematical
analysis,
singular
only,
definite
and
countable)
An
integral
which
has
more
general
application
than
that
of
the
Riemann
integral,
because
it
allows
the
region
of
integration
to
be
partitioned
into
not
just
intervals
but
any
measurable
sets
for
which
the
function
to
be
integrated
has
a
sufficiently
narrow
range.
(Formal
definitions
can
be
found
at
PlanetMath).
Japanese Meaning
ルベーグ積分：リーマン積分よりも広範な場合に適用可能な積分法であり、積分領域を単なる区間ではなく、測度可能な任意の集合に分割できるため、関数の値域が十分に限定される場合に積分が可能となる。
Sense（1）
(mathematical
analysis,
singular
only,
definite
and
countable)
An
integral
which
has
more
general
application
than
that
of
the
Riemann
integral,
because
it
allows
the
region
of
integration
to
be
partitioned
into
not
just
intervals
but
any
measurable
sets
for
which
the
function
to
be
integrated
has
a
sufficiently
narrow
range.
(Formal
definitions
can
be
found
at
PlanetMath).
（ plural ）
Quizzes for review
(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath).
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See correct answer
Lebesgue integral
To compute the expectation of the random variable rigorously, we used the Lebesgue integral over the probability space.
See correct answer
To compute the expectation of the random variable rigorously, we used the Lebesgue integral over the probability space.
音声機能が動作しない場合はこちらをご確認ください
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