-
positive measures. A
measure that has no
atoms is
called non-atomic or
atomless.
Given a
measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} and a measure...
-
possibility of "
atomless gunk",
which was
shortened to "gunk" by
later writers. Dean W.
Zimmerman defends the
possibility of
atomless gunk. If point-sized...
- term "simple" has
become the standard.
Simples are to be
contrasted with
atomless gunk (where
something is "gunky" if it is such that
every proper part has...
- this is the only
nontrivial Boolean algebra that is both
countable and
atomless. The
complete Cantor algebra is the
complete Boolean algebra of
Borel subsets...
- and the set of all real
algebraic numbers. any two
countably infinite atomless Boolean algebras are
isomorphic to each other. any two
equivalent countable...
-
Lebesgue measure to all sets of real
numbers if and only if
there is an
atomless probability measure on the
power set of some non-empty set.
Solovay (1971)...
-
representation theorem for
Boolean algebras) to the fact that any two
countable atomless Boolean algebras are isomorphic. As can be
expected from Brouwer's theorem...
- and
topological consequences: The
union of κ or
fewer null sets in an
atomless σ-finite
Borel measure on a
Polish space is null. In particular, the union...
- Fenchel, her dissertation, A
critical overview of the
present theory on
atomless economies, won a gold medal,
something which was used to
support young...
-
Presburger arithmetic,
algebraically closed fields, real
closed fields,
atomless Boolean algebras, term algebras,
dense linear orders,
abelian groups, random...
