Liouville theorem
E1549081
UNEXPLORED
Liouville's theorem is a fundamental result in Hamiltonian mechanics stating that the phase-space volume occupied by an ensemble of systems is conserved over time under Hamiltonian evolution.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Liouville theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T22666439 — 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: Liouville theorem Context triple: [Poisson bracket, appearsIn, Liouville theorem]
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A.
Liouville's theorem
Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
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B.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
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C.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
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D.
Borel–Carathéodory theorem
The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
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E.
Casorati–Weierstrass theorem
The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
- 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: Liouville theorem Target entity description: Liouville's theorem is a fundamental result in Hamiltonian mechanics stating that the phase-space volume occupied by an ensemble of systems is conserved over time under Hamiltonian evolution.
-
A.
Liouville's theorem
Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
-
B.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
-
C.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
-
D.
Borel–Carathéodory theorem
The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
-
E.
Casorati–Weierstrass theorem
The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.