Displaying similar documents to “A Lebesgue decomposition for elements in a topological group.”

On abstract Stieltjes measure

James E. Huneycutt Jr. (1971)

Annales de l'institut Fourier

Similarity:

In 1955, A. Revuz - Annales de l’Institut Fourier, vol. 6 (1955-56) - considered a type of Stieltjes measure defined on analogues of half-open, half-closed intervals in a partially ordered topological space. He states that these functions are finitely additive but his proof has an error. We shall furnish a new proof and extend some of this results to “measures” taking values in a topological abelian group.

Componentwise and Cartesian decompositions of linear relations

S. Hassi, H. S. V. de Snoo, F. H. Szafraniec

Similarity:

Let A be a, not necessarily closed, linear relation in a Hilbert space ℌ with a multivalued part mul A. An operator B in ℌ with ran B ⊥ mul A** is said to be an operator part of A when A = B +̂ ({0} × mul A), where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for an operator part are established...