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12 relations: Borel regular measure, Lebesgue measure, Mathematics, Measurable cardinal, Measure (mathematics), Polish space, Probability measure, Radon measure, Real line, Regularity theorem for Lebesgue measure, Sigma-algebra, Topological space.
Borel regular measure
In mathematics, an outer measure μ on n-dimensional Euclidean space Rn is called a Borel regular measure if the following two conditions hold.
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Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Measurable cardinal
In mathematics, a measurable cardinal is a certain kind of large cardinal number.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Polish space
In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset.
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Probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.
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Radon measure
In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Regularity theorem for Lebesgue measure
In mathematics, the regularity theorem for Lebesgue measure is a result in measure theory that states that Lebesgue measure on the real line is a regular measure.
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Sigma-algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Regular Borel measure, Μ-regular set.
