-
positive measures. A
measure which 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...
- 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...
- theory. He
became world-wide
known for his
theorem on the
range of an
atomless vector-measure in
finite dimensions, now
called the
Lyapunov Convexity...
- 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...
- 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...
-
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...
-
Boolean algebras: Atomic: ∀x x = 0 ∨ ∃y y ≤ x ∧ atom(y)
Atomless: ∀x ¬atom(x) The
theory of
atomless Boolean algebras is ω-categorical and complete. For any...
- In mathematics, a
Suslin algebra is a
Boolean algebra that is complete,
atomless,
countably distributive, and
satisfies the
countable chain condition. They...
-
Lebesgue measure, μsc is
singular with
respect to the
Lebesgue measure and
atomless, and μpp is a pure
point measure. A
usual presentation of the probability...
