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Locally integrable function and Lp space

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Locally integrable function and Lp space

Locally integrable function vs. Lp space

In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is finite) on every compact subset of its domain of definition. In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.

Similarities between Locally integrable function and Lp space

Locally integrable function and Lp space have 21 things in common (in Unionpedia): Banach space, Complete metric space, Complex number, Function (mathematics), Function space, Hölder's inequality, Indicator function, Integral, Lebesgue integration, Mathematics, Measurable function, Measure space, Nicolas Bourbaki, Norm (mathematics), Open set, Radon–Nikodym theorem, Real number, Sequence, Stefan Banach, Topological space, Topological vector space.

Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.

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Complete metric space

In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Function space

In mathematics, a function space is a set of functions between two fixed sets.

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Hölder's inequality

In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of ''Lp'' spaces.

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Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.

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Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Lebesgue integration

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.

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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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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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Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

Locally integrable function and Norm (mathematics) · Lp space and Norm (mathematics) · See more »

Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

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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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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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Stefan Banach

Stefan Banach (30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the world's most important and influential 20th-century mathematicians.

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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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Topological vector space

In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.

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The list above answers the following questions

Locally integrable function and Lp space Comparison

Locally integrable function has 73 relations, while Lp space has 127. As they have in common 21, the Jaccard index is 10.50% = 21 / (73 + 127).

References

This article shows the relationship between Locally integrable function and Lp space. To access each article from which the information was extracted, please visit:

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