Definition of Atomless. Meaning of Atomless. Synonyms of Atomless

- 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...
- 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...
- and the set of all real algebraic numbers. any two countably infinite atomless Boolean algebras are isomorphic to each other. any two equivalent countable...
- atoms, focusing on how such atomic parts combine to form larger wholes. atomless gunk See gunk. calculus of individuals Because mereology applies to individuals...
- 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...
- 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...
- Example 4, whence it is not atomless and therefore not isomorphic to Example 5/6. However it contains an infinite atomless subalgebra, namely Example 5...