Gauss measure
E1160949
UNEXPLORED
The Gauss measure is a probability measure on the unit interval that is invariant under the Gauss map used in continued fraction expansions, playing a central role in metric number theory and the study of constants like Khinchin's constant.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gauss measure canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T15502485 — 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: Gauss measure Context triple: [Khinchin's constant, relatedTo, Gauss measure]
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A.
Liouville measure
Liouville measure is a canonical volume measure on phase space in Hamiltonian mechanics and symplectic geometry that remains invariant under the system’s time evolution.
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B.
Haar measure
Haar measure is a fundamental concept in harmonic analysis and topological group theory, providing a translation-invariant way to assign measures to subsets of locally compact groups.
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C.
Piatetski-Shapiro measure
The Piatetski-Shapiro measure is a probability measure in harmonic analysis and representation theory introduced by Ilya Piatetski-Shapiro, used to study automorphic forms and related number-theoretic structures.
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D.
Stieltjes measure
A Stieltjes measure is a measure on the real line constructed from a nondecreasing, right-continuous function, providing the measure-theoretic foundation for the Riemann–Stieltjes and Lebesgue–Stieltjes integrals.
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E.
Lebesgue measure
Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
- 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: Gauss measure Target entity description: The Gauss measure is a probability measure on the unit interval that is invariant under the Gauss map used in continued fraction expansions, playing a central role in metric number theory and the study of constants like Khinchin's constant.
-
A.
Liouville measure
Liouville measure is a canonical volume measure on phase space in Hamiltonian mechanics and symplectic geometry that remains invariant under the system’s time evolution.
-
B.
Haar measure
Haar measure is a fundamental concept in harmonic analysis and topological group theory, providing a translation-invariant way to assign measures to subsets of locally compact groups.
-
C.
Piatetski-Shapiro measure
The Piatetski-Shapiro measure is a probability measure in harmonic analysis and representation theory introduced by Ilya Piatetski-Shapiro, used to study automorphic forms and related number-theoretic structures.
-
D.
Stieltjes measure
A Stieltjes measure is a measure on the real line constructed from a nondecreasing, right-continuous function, providing the measure-theoretic foundation for the Riemann–Stieltjes and Lebesgue–Stieltjes integrals.
-
E.
Lebesgue measure
Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.