-
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...
- 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...
- 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...
- 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...
-
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...
- Fenchel, her dissertation, A
critical overview of the
present theory on
atomless economies, won a gold medal,
something which was used to
support young...
- atoms,
focusing on how such
atomic parts combine to form
larger wholes.
atomless gunk See gunk.
calculus of
individuals Because mereology applies to individuals...
- z[Czx\leftrightarrow Czy]\rightarrow x=y.} All
regions have
proper parts, so that C is an
atomless theory. P.9. C4. ∃ y [ y < x ] . {\displaystyle \exists y[y<x].} Given...
