検索結果- 英語 - 英語
検索内容:
keeps measures
keep measures
verb
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).
measurable set
noun
Lebesgue measurable
adj
Lebesgue measure
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).
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