Lesson plan
Random element
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 who commented: [the] development of probability theory and expansion of area of its applications have led to necessity to pass from schemes where (random) outcomes of experiments can be described by number or a finite set of numbers, to schemes where outcomes of experiments 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.
Article summary
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 who commented: [the] development of probability theory and expansion of area of its applications have led to necessity to pass from schemes where (random) outcomes of experiments can be described by number or a finite set of numbers, to schemes where outcomes of experiments 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.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.