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Everything about Hyperfinite set
Type of internal set in nonstandard analysis
In nonstandard analysis, a branch of mathematics, a hyperfinite set or *-finite set is a type of internal set. An internal set H of internal cardinality g ∈ *N is hyperfinite if and only if there exists an internal bijection between G = {1,2,3,...,g} and H. Hyperfinite sets share the properties of finite sets: A hyperfinite set has minimal and maximal elements, and a hyperfinite union of a hyperfinite collection of hyperfinite sets may be derived. The sum of the elements of any hyperfinite subset of *R always exists, leading to the possibility of well-defined integration. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Hyperfinite setA 5-minute orientation
- Skim a recent paper: Linear Diophantine HyperFuzzy Set and SuperHyperFuzzy SetInfluential work since 2022
- Read the landmark paper: Descriptive set theory over hyperfinite setsCited 22 times
- Go sideways: Internal setA closely related topic
- Go sideways: Standard part functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Descriptive set theory over hyperfinite sets
Meager sets on the hyperfinite time line
Some results about Borel sets in descriptive set theory of hyperfinite sets
Analytic mappings on hyperfinite sets
Analytic Mappings on Hyperfinite Sets
A Theory of Hyperfinite Sets
Previsible sets for hyperfinite filtrations
🆕 Influential since 2022
📚 Books worth reading
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🔗 Related topics
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