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35 relations: American Journal of Mathematics, Borel measure, Connected space, Countable set, Counting measure, Decomposable measure, Disjoint sets, Equivalence (measure theory), Finite measure, Fubini's theorem, Haar measure, Hausdorff dimension, Hausdorff measure, Integer, Interval (mathematics), Lebesgue measure, Lie group, Locally compact group, Locally finite measure, Mathematics, Measurable function, Measurable space, Measure (mathematics), Measure space, Metric space, Null set, Radon–Nikodym theorem, Real number, S-finite measure, Separable space, Set (mathematics), Sigma additivity, Sigma-algebra, Signed measure, Union (set theory).
American Journal of Mathematics
The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.
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Borel measure
In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets).
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Counting measure
In mathematics, the counting measure is an intuitive way to put a measure on any set: the "size" of a subset is taken to be: the number of elements in the subset if the subset has finitely many elements, and ∞ if the subset is infinite.
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Decomposable measure
In mathematics, a decomposable measure is a measure that is a disjoint union of finite measures.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Equivalence (measure theory)
In mathematics, and specifically in measure theory, equivalence is a notion of two measures being qualitatively similar.
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Finite measure
In measure theory, a branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values.
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Fubini's theorem
In mathematical analysis Fubini's theorem, introduced by, is a result that gives conditions under which it is possible to compute a double integral using iterated integrals.
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Haar measure
In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups.
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Hausdorff dimension
Hausdorff dimension is a measure of roughness in mathematics introduced in 1918 by mathematician Felix Hausdorff, and it serves as a measure of the local size of a space, taking into account the distance between its points.
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Hausdorff measure
In mathematics a Hausdorff measure is a type of outer measure, named for Felix Hausdorff, that assigns a number in to each set in Rn or, more generally, in any metric space.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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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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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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Locally compact group
In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff.
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Locally finite measure
In mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure.
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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 function
In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open.
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Measurable space
In mathematics, a measurable space or Borel space is a basic object in measure theory.
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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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Measure space
A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Null set
In set theory, a null set N \subset \mathbb is a set that can be covered by a countable union of intervals of arbitrarily small total length.
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Radon–Nikodym theorem
In mathematics, the Radon–Nikodym theorem is a result in measure theory.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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S-finite measure
In measure theory, a branch of mathematics that studies generalized notions of volumes, an s-finite measure is a special type of measure.
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Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Sigma additivity
In mathematics, additivity and sigma additivity (also called countable additivity) of a function defined on subsets of a given set are abstractions of the intuitive properties of size (length, area, volume) of a set.
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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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Signed measure
In mathematics, signed measure is a generalization of the concept of measure by allowing it to have negative values.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Redirects here:
Moderate measure, Sigma finite measure, Sigma-finite, Sigma-finite measure, Σ-finite.
References
[1] https://en.wikipedia.org/wiki/Σ-finite_measure
