Last Updated：2025/11/26
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To compute the expectation of the random variable rigorously, we used the Lebesgue integral over the probability space.
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To compute the expectation of the random variable rigorously, we used the Lebesgue integral over the probability space.
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Related words
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。
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