Hardy–Littlewood–Pólya inequality
E1247123
UNEXPLORED
The Hardy–Littlewood–Pólya inequality is a fundamental result in majorization theory and inequalities that characterizes how convex functions behave under rearrangements of sequences or vectors.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Hardy–Littlewood–Pólya "Inequalities" | 1 |
| Hardy–Littlewood–Pólya inequality canonical | 1 |
| Hardy–Littlewood–Pólya theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T17020102 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood–Pólya inequality Context triple: [Karamata's inequality, generalizes, Hardy–Littlewood–Pólya inequality]
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A.
Chebyshev’s sum inequality
Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
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B.
Karamata's inequality
Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
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C.
Maclaurin’s inequality in symmetric means
Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
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D.
Hardy inequality
The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
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E.
Riesz rearrangement inequality
The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood–Pólya inequality Target entity description: The Hardy–Littlewood–Pólya inequality is a fundamental result in majorization theory and inequalities that characterizes how convex functions behave under rearrangements of sequences or vectors.
-
A.
Chebyshev’s sum inequality
Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
-
B.
Karamata's inequality
Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
-
C.
Maclaurin’s inequality in symmetric means
Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
-
D.
Hardy inequality
The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
-
E.
Riesz rearrangement inequality
The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hardy–Littlewood–Pólya theorem
this entity surface form:
Hardy–Littlewood–Pólya "Inequalities"