In mathematics — specifically, in geometric measure theory — a uniformly distributed measure on a metric space is one for which the measure of an open ball depends only on its radius and not on its centre. By convention, the measure is also required to be Borel regular, and to take positive and finite values on open balls of finite radius. Thus, if (X, d) is a metric space, a Borel regular measure μ on X is said to be uniformly distributed if
for all points x and y of X and all 0 < r < +∞, where
and 22 Related for: Uniformly distributed measure information
it turns out, uniformlydistributedmeasures are very rigid objects. On any "decent" metric space, the uniformlydistributedmeasures form a one-parameter...
s2, s3, ...) of real numbers is said to be equidistributed, or uniformlydistributed, if the proportion of terms falling in a subinterval is proportional...
which are effectively distributed according to the standard uniform distribution. On the other hand, the uniformlydistributed numbers are often used...
Distributed computing is a field of computer science that studies distributed systems, defined as computer systems whose inter-communicating components...
{\displaystyle F} by means of the empirical measure or empirical distribution function, respectively. These are uniformly good estimates under certain conditions...
theorem is the statement that the sequence a, 2a, 3a, ... mod 1 is uniformlydistributed on the circle R / Z {\displaystyle \mathbb {R} /\mathbb {Z} } ,...
number generator that produces numbers X {\displaystyle X} that are uniformlydistributed in the half-open interval [0, 1). These random variates X {\displaystyle...
same measure on Sn follows from an elegant result of Christensen: all these measures are obviously uniformlydistributed on Sn, and any two uniformly distributed...
non-uniform in f. The notion of total variation convergence formalizes the assertion that the measure of all measurable sets should converge uniformly, i...
ergodic is equivalent to the statement that the real numbers are uniformlydistributed. The set of all such strings can be written in a variety of ways:...
and are thus uniformly randomly distributed. If individuals are aggregated, then its value approaches 0, and if they are randomly distributed, the value...
of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample...
phenomena and tools used to measure them generally feature asymmetries and systematic biases that make their outcomes not uniformly random. A randomness extractor...
way to generate the Cauchy-distributed example is where the random numbers equal the tangent of an angle uniformlydistributed between −90° and +90°. The...
percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution....
In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral...
of classical discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some (mostly geometrically...
{\displaystyle {\frac {k}{\lambda }}.} Erlang-distributed random variates can be generated from uniformlydistributed random numbers ( U ∈ [ 0 , 1 ] {\displaystyle...
on the circle in terms of measure theory, the forward orbit of z is dense in the circle, and in fact uniformlydistributed on the circle. There are also...
producing uniform random variates. The most straightforward method is based on the probability integral transform property: if U is distributeduniformly on...
studies on pair programming." It concluded that "pair programming is not uniformly beneficial or effective." Although pair programmers may complete a task...
\sigma ^{2}<\infty } . Moreover, X {\displaystyle \mathbf {X} } is uniformlydistributed on [ 0 , 1 ] d {\displaystyle [0,1]^{d}} and m {\displaystyle m}...
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