Lectures on Ergodic Theory
E325280
"Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lectures on Ergodic Theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3072658 — 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: Lectures on Ergodic Theory Context triple: [Annals of Mathematics Studies, hasNotableWork, Lectures on Ergodic Theory]
-
A.
Kakutani equivalence in ergodic theory
Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
-
B.
Kakutani’s random ergodic theorem
Kakutani’s random ergodic theorem is a fundamental result in ergodic theory that extends classical ergodic theorems to sequences of randomly chosen measure-preserving transformations.
-
C.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
D.
Kolmogorov zero–one law
The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
-
E.
Lyapunov exponents
Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
- 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: Lectures on Ergodic Theory Target entity description: "Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical systems.
-
A.
Kakutani equivalence in ergodic theory
Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
-
B.
Kakutani’s random ergodic theorem
Kakutani’s random ergodic theorem is a fundamental result in ergodic theory that extends classical ergodic theorems to sequences of randomly chosen measure-preserving transformations.
-
C.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
D.
Kolmogorov zero–one law
The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
-
E.
Lyapunov exponents
Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ non‑fiction work ⓘ |
| academicDiscipline | mathematics ⓘ |
| author |
Paul Halmos
ⓘ
Paul Halmos ⓘ
surface form:
Paul R. Halmos
|
| category |
books on dynamical systems
ⓘ
books on ergodic theory ⓘ books on mathematics ⓘ |
| field |
dynamical systems
ⓘ
ergodic theory ⓘ measure theory ⓘ probability theory ⓘ |
| focus |
foundations of ergodic theory
ⓘ
systematic development of ergodic theory ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
researchers in dynamical systems ⓘ researchers in ergodic theory ⓘ |
| language | English ⓘ |
| notableFor |
influence on the development of modern ergodic theory
ⓘ
systematic treatment of classical ergodic theorems ⓘ |
| style |
lecture‑note format
ⓘ
rigorous exposition ⓘ |
| subject |
Bernoulli shifts
ⓘ
ergodic theorem ⓘ
surface form:
Birkhoff ergodic theorem
Kolmogorov–Sinai entropy ⓘ Kronecker systems ⓘ ergodic theorems ⓘ ergodic transformations ⓘ invariant measures ⓘ measure algebras ⓘ measure‑preserving transformations ⓘ measure‑theoretic dynamical systems ⓘ metric isomorphism in ergodic theory ⓘ mixing transformations ⓘ probability‑preserving transformations ⓘ recurrence in dynamical systems ⓘ spectral theory of measure‑preserving transformations ⓘ strong mixing ⓘ unitary operators associated with dynamical systems ⓘ ergodic theorem ⓘ
surface form:
von Neumann mean ergodic theorem
weak mixing ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lectures on Ergodic Theory Description of subject: "Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.