specifically in measure theory, equivalence is a notion of two measures being qualitatively similar. Specifically, the two measures agree on which events...

In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff...

The Ricardian equivalence proposition (also known as the Ricardo–de Viti–Barro equivalence theorem) is an economic hypothesis holding that consumers are...

derivative, or density, of the absolutely continuous measure μ . {\displaystyle \mu .} Equivalence between (1), (2) and (3) holds also in R n {\displaystyle...

Anosov, D.V. (2001) [1994], "Measure space", Encyclopedia of Mathematics, EMS Press Segal, I. E. (1951). "Equivalences of Measure Spaces". American Journal...

In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame. The two differ only by a multiplicative constant...

fall and requires the weak equivalence to be valid everywhere. This form was a critical input for the development of the theory of general relativity. The...

In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences...

Supporting measure may refer to a σ-finite equivalent measure, see Equivalence (measure theory)#Supporting measure a special measure in the context of...

In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the...

\int _{X}^{\oplus }H_{x}\ d\mu (x).} The measure class[clarification needed] of μ and the measure equivalence class of the multiplicity function x → dim...

In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X (in the product topology)...

In set theory, a normal measure is a measure on a measurable cardinal κ such that the equivalence class of the identity function on κ maps to κ itself...

measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving...

precisely in measure theory, an atom is a measurable set that has positive measure and contains no set of smaller positive measures. A measure that has no...

descriptive set theory and related areas of mathematics, a hyperfinite equivalence relation on a standard Borel space X is a Borel equivalence relation E with...

additive. In the theory of vector measures, Lyapunov's theorem states that the range of a (non-atomic) finite-dimensional vector measure is closed and convex...

topological boundary has Lebesgue measure zero. (Or equivalently, if the boundary has Jordan measure zero; the equivalence holds due to compactness of the...

in the same equivalence class. There are three fundamental approaches to constructing measures of network similarity: structural equivalence, automorphic...

general spaces, measure spaces, such as those that arise in probability theory. The term Lebesgue integration can mean either the general theory of integration...

order and an equivalence relation because it satisfies both the antisymmetry property of partial orders and the symmetry property of equivalence relations...

comparing sets. Measure theory provides a more nuanced theory of size that conforms to our intuition that length and area are incompatible measures of size....

exponential equivalence of measures is how two sequences or families of probability measures are "the same" from the point of view of large deviations theory. Let...

(GP-A) was a space-based experiment to test the equivalence principle, a feature of Einstein's theory of relativity. It was performed jointly by the Smithsonian...

for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula E = mc2, which...

defined in three equivalent ways. One way uses an effective analogue of measure theory; another uses effective martingales. The third way defines an infinite...

perfect recall for outcome equivalence, and its impact on normal and extended form games. Nash equilibrium Haven (graph theory) Evolutionarily stable strategy...

theoretical physics is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example...

In measure theory, a branch of mathematics, Kakutani's theorem is a fundamental result on the equivalence or mutual singularity of countable product measures...

measure theory, there are various notions of the convergence of measures. For an intuitive general sense of what is meant by convergence of measures,...