In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization...

In data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the...

operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is...

In mathematics, measure theory in topological vector spaces refers to the extension of measure theory to topological vector spaces. Such spaces are often...

representation theorem. Angular displacement Complex measure Spectral measure Vector measure Riesz–Markov–Kakutani representation theorem Signed arc...

Outer measure Product measure Pushforward measure Regular measure Vector measure Valuation (measure theory) Volume form One way to rephrase our definition...

transform of a measure applied to the associated Stieltjes measure, the conventional Laplace transform cannot handle vector measures: measures with values...

limit theorem Lyapunov vector-measure theorem, theorem in measure theory that the range of any real-valued, non-atomic vector measure is compact and convex...

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...

complex measures is a Banach space. Riesz representation theorem Signed measure Vector measure Tao, Terence (2011-09-14). An Introduction to Measure Theory...

(generally vector valued) random variables X n {\displaystyle X_{n}} . The diffuse component μ d {\displaystyle \mu _{d}} is null for a counting measure. In...

A vector signal analyzer is an instrument that measures the magnitude and phase of the input signal at a single frequency within the IF bandwidth of the...

In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite...

distance-vector routing protocol in data networks determines the best route for data packets based on distance. Distance-vector routing protocols measure the...

quantum mechanics Density matrix Quantum operation Projection-valued measure Vector measure Peres, Asher; Terno, Daniel R. (2004). "Quantum information and...

cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional vector space....

} is a signed measure: its total variation is defined as above. This definition works also if μ {\displaystyle \mu } is a vector measure: the variation...

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...

operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces...

point, the zero vector is called the origin. Adding a fixed vector to the elements of a linear subspace (vector subspace) of a vector space produces an...

A vector measuring current meter (VMCM) is an instrument used for obtaining measurements of horizontal velocity in the upper ocean, which exploits two...

function Pettis integral Vector measure Weakly measurable function Diestel, Joseph; Uhl, Jr., John Jerry (1977). Vector Measures. Mathematical Surveys....

ξ {\displaystyle \xi } is a unit vector. Example Let ( X , M , μ ) {\displaystyle (X,M,\mu )} be a σ-finite measure space and, for all E ∈ M {\displaystyle...

used for those measuring greater than 1 mT. There are two basic types of magnetometer measurement. Vector magnetometers measure the vector components of...

the measure of units between a number and zero. In vector spaces, the Euclidean norm is a measure of magnitude used to define a distance between two points...

larger this rate of change. In other words, the curvature measures how fast the unit tangent vector to the curve at point P rotates when point P moves at...

(usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used...

finite-dimensional p norm spaces - Vector spaces of measurable functions: the L p {\displaystyle L^{p}} spaces Measure-preserving dynamical system – Subject...

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...

Hebrew University. His MSc thesis was on the subject of “The Range of a Vector Measure” and was supervised by Joram Lindenstrauss. His PhD thesis, "Values...