-
definitions of
measurability, such as weak
measurability and
Bochner measurability, exist.
Random variables are by
definition measurable functions defined...
-
relationship between measurability and weak
measurability is
given by the
following result,
known as Pettis'
theorem or
Pettis measurability theorem. Function...
- In mathematics,
progressive measurability is a
property in the
theory of
stochastic processes. A
progressively measurable process,
while defined quite...
- In mathematics, a
measurable space or
Borel space is a
basic object in
measure theory. It
consists of a set and a σ-algebra,
which defines the subsets...
- In mathematics, a non-
measurable set is a set
which cannot be ****igned a
meaningful "volume". The
existence of such sets is
construed to
provide information...
-
relationship between measurability and weak
measurability is
given by the
following result,
known as Pettis'
theorem or
Pettis measurability theorem. A function...
-
values in a
Banach space (or Fréchet space),
strong measurability usually means Bochner measurability. However, if the
values of f lie in the
space L (...
-
alternative definition of
Lebesgue measurability. More precisely, E ⊂ R {\displaystyle E\subset \mathbb {R} } is Lebesgue-
measurable if and only if for
every ε...
- a
measurable set. The Carathéodory
criterion is of
considerable importance because, in
contrast to Lebesgue's
original formulation of
measurability, which...
- {\displaystyle (X,\Sigma )} is
called a
measurable space, and the
members of Σ {\displaystyle \Sigma } are
called measurable sets. A
triple ( X , Σ , μ ) {\displaystyle...
