In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that for any measurable space ( X , Σ ) {\displaystyle...

In mathematics, Jordan decomposition may refer to Hahn decomposition theorem, and the Jordan decomposition of a measure Jordan normal form of a matrix...

part. Decomposition of spectrum Hahn decomposition theorem and the corresponding Jordan decomposition theorem (Halmos 1974, Section 32, Theorem C) (Hewitt...

Hahn–Banach theorem and (independently of Banach and Steinhaus) the uniform boundedness principle. Other theorems include: the Hahn decomposition theorem; the...

the Hahn decomposition theorem is called the Jordan decomposition. The measures μ+, μ− and |μ| are independent of the choice of P and N in the Hahn decomposition...

functions Hahn decomposition theorem of a measure space Jordan decomposition theorem of a signed measure Helmholtz decomposition, decomposition of a vector...

hold, and therefore, μ ( E ) = 0. {\displaystyle \mu (E)=0.} The Hahn decomposition theorem states that for every measurable space ( X , Σ ) {\displaystyle...

spaces. The spectral theorem also provides a canonical decomposition, called the spectral decomposition, of the underlying vector space on which the operator...

three-lines theorem (complex analysis) Hadwiger's theorem (geometry, measure theory) Hahn decomposition theorem (measure theory) Hahn embedding theorem (ordered...

is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists a decomposition of the...

the Hopf extension theorem and the Hahn–Kolmogorov extension theorem. Several very similar statements of the theorem can be given. A slightly more involved...

to this decomposition of a function, one may decompose a signed measure into positive and negative parts — see the Hahn decomposition theorem. Rectifier...

is the required function. Lebesgue's decomposition theorem shows that the assumptions of the Radon–Nikodym theorem can be found even in a situation which...

:\Sigma \to [-\infty ,+\infty ]} is a signed measure. Use the Hahn decomposition theorem to write μ = μ + − μ − , {\displaystyle \mu =\mu ^{+}-\mu ^{-}...

paradox, the Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. Stefan...

Partial fraction decomposition over R Vieta's formulas Integer-valued polynomial Algebraic equation Factor theorem Polynomial remainder theorem See also Theory...

S2CID 119301206. Gowers, Timothy (2010). "Decompositions, approximate structure, transference, and the Hahn–Banach theorem". Bulletin of the London Mathematical...

more. Hahn series are a further (larger) generalization of Puiseux series, introduced by Hans Hahn in the course of the proof of his embedding theorem in...

Hadwiger's theorem – Theorem in integral geometry Hahn decomposition theorem – Measurability theorem Invariant measure Lebesgue's decomposition theorem Positive...

upper and lower variations to prove the Hahn–Jordan decomposition: according to his version of this theorem, the upper and lower variation are respectively...

to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition. Such statements can be rephrased...

This proves the theorem. It follows from the above decomposition that A* is the linear span of states. By the Krein-Milman theorem, the state space of...

Wold contributed the Cramér–Wold theorem characterizing the normal distribution and developed the Wold decomposition in time series analysis. In microeconomics...

as the decomposition of the squared length of a vector into the sum of the squared lengths of several vectors, using the Pythagorean Theorem." The theory...

measure μ are finite-valued signed measures. One can apply the Hahn-Jordan decomposition to these measures to split them as μ 1 = μ 1 + − μ 1 − {\displaystyle...

property that is held by all cards). decomposition See tree decomposition, path decomposition, or branch-decomposition. degenerate degeneracy A k-degenerate...

compounds under Otto Hahn and Lise Meitner. He received his Ph.D. at Stuttgart with Prof. Erich Regener for work on the decomposition of ozone. Hellmann's...

about how close the approximation is. For example, the Shapley–Folkman theorem provides an upper bound on the distance between any point in the Minkowski...

p)-forms. Using the Hahn–Banach theorem, Harvey and Lawson proved the following criterion of existence of Kähler metrics. Theorem: Let M be a compact...

{W}}=W^{\perp \perp }.} This is a rather straightforward consequence of the Hahn–Banach theorem. In special relativity the orthogonal complement is used to determine...