In probability theory, random element is a generalization of the concept of random variable to more complicated spaces than the simple real line. The concept was introduced by Maurice Fréchet (1948) who commented that the “development of probability theory and expansion of area of its applications have led to necessity to pass from schemes where (random) outcomes of experience can be described by number or a finite set of numbers, to schemes where outcomes of experience represent, for example, vectors, functions, processes, fields, series, transformations, and also sets or collections of sets.”
The modern day usage of “random element” frequently assumes the space of values is a topological vector space, often a Banach or Hilbert space with a specified natural sigma algebra of subsets.
Read more about Random Element: Definition, List of Different Types of Random Elements
Famous quotes containing the words random and/or element:
“Assemble, first, all casual bits and scraps
That may shake down into a world perhaps;
People this world, by chance created so,
With random persons whom you do not know—”
—Robert Graves (1895–1985)
“One can describe a landscape in many different words and sentences, but one would not normally cut up a picture of a landscape and rearrange it in different patterns in order to describe it in different ways. Because a photograph is not composed of discrete units strung out in a linear row of meaningful pieces, we do not understand it by looking at one element after another in a set sequence. The photograph is understood in one act of seeing; it is perceived in a gestalt.”
—Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)