This list could be expanded to include most fields of mathematics, including measure theory, ergodic theory, probability, representation theory, and differential geometry.

Occasionally, " almost all " is used in the sense of " almost everywhere " in measure theory, or in the closely related sense of " almost surely " in probability theory.

In algorithmic information theory ( a subfield of computer science ), the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object.

In mathematics, specifically in measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of X ; this is known as the σ-algebra of Borel sets.

Category: Measures ( measure theory )

In Geometric measure theory such a smooth curve as the circle that can be approximated by small straight segments with a definite limit is termed a rectifiable curve.

This is totally spurious, since no matter who measured first the other will measure the opposite spin despite the fact that ( in theory ) the other has a 50 % ' probability ' ( 50: 50 chance ) of measuring the same spin, unless data about the first spin measurement has somehow passed faster than light ( of course TI gets around the light speed limit by having information travel backwards in time instead ).

Other major critiques are that the term is not defined well, and employs further terms that are not defined well, and therefore lacks explanatory power, that cultural imperialism is hard to measure, and that the theory of a legacy of colonialism is not always true.

The field of recursion theory, meanwhile, categorizes undecidable decision problems by Turing degree, which is a measure of the noncomputability inherent in any solution.

Null set was once a common synonym for " empty set ", but is now a technical term in measure theory.

Felix Hausdorff ( November 8, 1868 – January 26, 1942 ) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.

An important part of functional analysis is the extension of the theory of measure, integration, and probability to infinite dimensional spaces, also known as infinite dimensional analysis.

Graph theory is also widely used in sociology as a way, for example, to measure actors ' prestige or to explore diffusion mechanisms, notably through the use of social network analysis software.

* Information theory and measure theory

In information theory, entropy is a measure of the uncertainty associated with a random variable.

In probability theory and statistics, kurtosis ( from the Greek word κυρτός, kyrtos or kurtos, meaning bulging ) is any measure of the " peakedness " of the probability distribution of a real-valued random variable.

* Lambda denotes the Lebesgue measure in mathematical set theory.

** The Lebesgue measure of a countable disjoint union of measurable sets is equal to the sum of the measures of the individual sets.

* Hence, the set of algebraic numbers has Lebesgue measure zero ( as a subset of the complex numbers ), i. e. " almost all " complex numbers are not algebraic.

In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable.

When speaking about the reals, sometimes it means " all reals but a set of Lebesgue measure zero " ( formally, almost everywhere ).

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

To clarify, when one says that the Lebesgue measure is an extension of the Borel measure, it means that every Borel measurable set E is also a Lebesgue measurable set, and the Borel measure and the Lebesgue measure coincide on the Borel sets ( i. e., for every Borel measurable set ).

This measure was so named after Kim Jong Il made an inspection tour of an exhibition of light industrial products held in Pyongyang on August 3, 1984.

The " Dobson unit ", a convenient measure of the columnar density of ozone overhead, is named in his honor.

Another measure of the difference between these two similarly named but very distinct awards is their per-capita frequency of award: from 1946 to 1961 the average annual incidence of award of the Medal of Freedom was approximately 1 per every 86, 500 adult U. S. citizens ; from 1996 to 2011 the average annual incidence of award of the Presidential Medal of Freedom was approximately 1 per every 20, 500, 000 adult U. S. citizens ( so on an annualized per capita basis, about 240 Medals of Freedom have been awarded per one Presidential Medal of Freedom ).

In economics the Pareto index, named after the Italian economist and sociologist Vilfredo Pareto, is a measure of the breadth of income or wealth distribution.

As a further insurance measure against both radical designs failing, in July 1947 the Air Ministry issued Specification B. 9 / 48 written around Vickers-Armstrongs ' more conservative design, later named Valiant ; work began in April 1948.

Years later, Knef's first husband, an American named Kurt Hirsch, encouraged her to try again for success in the U. S. She changed her name from Knef to Neff and achieved a measure of stardom on Broadway as “ Ninotchka ” in the Cole Porter musical,

Macadie invented an instrument which could measure amperes ( amps ), volts and ohms, so the multifunctional meter was then named Avometer.

The geometrids, also known as inchworms or loopers, are so named because of the way they move, appearing to measure the earth ( the word geometrid means earth-measurer in Greek ); the primary reason for this unusual locomotion is the elimination of nearly all the prolegs except the clasper on the terminal segment.

The unit is named after Blaise Pascal, the eminent French mathematician, physicist, and philosopher noted for his experiments with a barometer, an instrument to measure air pressure.

Kaldor – Hicks efficiency, named for Nicholas Kaldor and John Hicks, also known as Kaldor – Hicks criterion, is a measure of economic efficiency that captures some of the intuitive appeal of Pareto efficiency, but has less stringent criteria and is hence applicable to more circumstances.

Another example is a sports bar at the bottom of 5th Street in Benicia, California, named " Bottom of the Fifth ", referring to ( 1 ) the address, ( 2 ) baseball's fifth inning, and ( 3 ) a measure of consumption of a common quantity of alcoholic beverage.

" King Richard is believed to have named him his heir as a temporary measure only to please his dying queen, who survived her own son's death by less than a year.

The sverdrup, named in honour of the pioneering oceanographer Harald Sverdrup, is a unit of measure of volume transport.

* Brewster ( unit ), a unit of measure named after David Brewster

* Clapham Junction railway station, by at least one measure — passenger interchanges — the busiest station in the United Kingdom and named after the neighbouring town of Clapham although it lies in the geographic heart of Battersea, SW11.

The balance that he used, made by a craftsman named Harrison, was the first of the precision balances of the 18th century, and as accurate as Lavoisier's ( which has been estimated to measure one part in 400, 000 ).

On November 6, 2007, voters approved by a vote of 1, 816 to 693 a measure that changed the township's name from Washington Township, which is the name of five other municipalities in New Jersey, to Robbinsville, named after a settlement within the township.

It is named after Oliver R. Smoot, a fraternity pledge to Lambda Chi Alpha, who in October 1958 lay on the Harvard Bridge ( between Boston and Cambridge, Massachusetts ), and was used by his fraternity brothers to measure the length of the bridge.

In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter ( rho ) or as, is a non-parametric measure of statistical dependence between two variables.

Following a mandate imposed on humanity by the Core requiring everyone to undergo patterning as a public health measure, a rebel band is formed out of colonies from the edges of the galaxy ( hence named the Arm ), whose members refused to leave their natural bodies to join the Core's machines.

In probability theory, the Girsanov theorem ( named after Igor Vladimirovich Girsanov ) describes how the dynamics of stochastic processes change when the original measure is changed to an equivalent probability measure.