Definition
Let be a topological vector space. Let be an index set and for all .
The series is called unconditionally convergent to, if
- the indexing set is countable and
- for every permutation of the relation holds:
Read more about this topic: Unconditional Convergence
Famous quotes containing the word definition:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on life (based on wording in the First Edition, 1935)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (18421910)
“... we all know the wags definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)