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If is a subset of a real or complex vector space, then the Minkowski functional or gauge of is defined to be the function: [,], valued in the extended real numbers, defined by ():= {: >}, where the infimum of the empty set is defined to be positive infinity (which is not a real number so that () would then not be real-valued).
the gauge as used in the definition of the Henstock-Kurzweil integral, also known as the gauge integral; in fractal geometry, a synonym for dimension function; in control theory and dynamical systems, a synonym for Lyapunov candidate function; in gauge theory, a synonym for gauge symmetry. a type of Minkowski functional
Because of this analogy, the term semimetric space (which has a different meaning in topology) is sometimes used as a synonym, especially in functional analysis. When a topology is generated using a family of pseudometrics, the space is called a gauge space.
In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple " diameter to the dimension " power law used in the construction of s -dimensional Hausdorff measure .
A particular choice of the scalar and vector potentials is a gauge (more precisely, gauge potential) and a scalar function ψ used to change the gauge is called a gauge function. [citation needed] The existence of arbitrary numbers of gauge functions ψ(r, t) corresponds to the U(1) gauge freedom of this theory. Gauge fixing can be done in many ...
Bore gauge: a device used for measuring holes. Hole gauge [3] used to gage internal dimensions of bores that are either too small in diameter for an inside micrometer, and have greater economy than a bore gage or other precision internal gage. Caliper: a device used to measure the distance between two opposing sides of an object.
The multidisciplinary artist recognizes something in a bag that's always been present in his personal style: utility.
Gauge block, a metal or ceramic block of precisely known dimension, used in measuring; Sight glass, also known as a water gauge, for measuring liquid level heights in storage tanks and pressure vessels; Boost gauge, a gauge used in conjunction with turbo-super-chargers; Pressure gauge or vacuum gauge, see pressure measurement