Mathematical Foundations of Information Theory
E378999
Mathematical Foundations of Information Theory is a seminal monograph by Aleksandr Khinchin that rigorously develops the probabilistic and mathematical basis of Shannon’s information theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Mathematical Foundations of Information Theory canonical | 1 |
| mathematical foundations of information theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3677828 — 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: Mathematical Foundations of Information Theory Context triple: [Aleksandr Khinchin, notableWork, Mathematical Foundations of Information Theory]
-
A.
An Introduction to Information Theory: Symbols, Signals and Noise
An Introduction to Information Theory: Symbols, Signals and Noise is a classic, accessible textbook that explains the fundamental concepts of information theory, communication, and coding for a broad scientific and engineering audience.
-
B.
A Mathematical Theory of Communication
A Mathematical Theory of Communication is Claude Shannon’s landmark 1948 paper that founded information theory by rigorously defining concepts like information, entropy, and channel capacity.
-
C.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
-
D.
information theory
Information theory is a mathematical framework for quantifying information, communication, and data compression, foundational to modern digital communication and signal processing.
-
E.
Communication Theory of Secrecy Systems
Communication Theory of Secrecy Systems is Claude Shannon’s foundational paper that established the mathematical basis of modern cryptography and information-theoretic security.
- 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: Mathematical Foundations of Information Theory Target entity description: Mathematical Foundations of Information Theory is a seminal monograph by Aleksandr Khinchin that rigorously develops the probabilistic and mathematical basis of Shannon’s information theory.
-
A.
An Introduction to Information Theory: Symbols, Signals and Noise
An Introduction to Information Theory: Symbols, Signals and Noise is a classic, accessible textbook that explains the fundamental concepts of information theory, communication, and coding for a broad scientific and engineering audience.
-
B.
A Mathematical Theory of Communication
A Mathematical Theory of Communication is Claude Shannon’s landmark 1948 paper that founded information theory by rigorously defining concepts like information, entropy, and channel capacity.
-
C.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
-
D.
information theory
Information theory is a mathematical framework for quantifying information, communication, and data compression, foundational to modern digital communication and signal processing.
-
E.
Communication Theory of Secrecy Systems
Communication Theory of Secrecy Systems is Claude Shannon’s foundational paper that established the mathematical basis of modern cryptography and information-theoretic security.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
monograph ⓘ |
| aimsTo |
clarify the probabilistic basis of information measures
ⓘ
provide rigorous mathematical foundations for Shannon’s information theory ⓘ |
| author |
A. Ya. Khinchin
ⓘ
linked to:
Khinchin
Aleksandr Yakovlevich Khinchin ⓘ
linked to:
Aleksandr Khinchin
|
| basedOn |
measure theory
ⓘ
probability distributions ⓘ random variables ⓘ |
| centralConcept |
Shannon entropy
ⓘ
additivity of information ⓘ conditional information ⓘ information inequality ⓘ information measure ⓘ law of large numbers in information theory ⓘ mutual information ⓘ |
| field |
information theory
ⓘ
mathematics ⓘ probability theory ⓘ |
| focusesOn |
axiomatic derivation of entropy
ⓘ
probabilistic models of communication ⓘ properties of information measures ⓘ rigorous mathematical treatment of information ⓘ |
| genre |
mathematics textbook
ⓘ
scientific monograph ⓘ |
| hasApproach |
axiomatic approach to information
ⓘ
measure-theoretic rigor ⓘ probabilistic approach to information ⓘ |
| historicalPeriod | mid-20th century mathematics ⓘ |
| influenced |
rigorous development of information theory in mathematics
ⓘ
subsequent textbooks on information theory ⓘ |
| influencedBy |
Claude E. Shannon
ⓘ
linked to:
Claude Shannon
Shannon’s 1948 papers on information theory ⓘ
linked to:
A Mathematical Theory of Communication
|
| notableFor |
influencing later formalizations of information measures
ⓘ
rigorous derivation of Shannon entropy from axioms ⓘ systematic probabilistic framework for information ⓘ |
| originalLanguage | Russian ⓘ |
| recognizedAs |
classic text in mathematical information theory
ⓘ
seminal work in information theory ⓘ |
| relatedTo |
coding theory
ⓘ
communication theory ⓘ statistical mechanics (via entropy concepts) ⓘ |
| subject |
Shannon information theory
ⓘ
linked to:
information theory
entropy ⓘ ergodic theory (in relation to information) ⓘ measure-theoretic probability ⓘ probabilistic foundations of information ⓘ |
| usedIn |
advanced courses in probability and statistics
ⓘ
graduate-level courses in information theory ⓘ |
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: Mathematical Foundations of Information Theory Description of subject: Mathematical Foundations of Information Theory is a seminal monograph by Aleksandr Khinchin that rigorously develops the probabilistic and mathematical basis of Shannon’s information theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Mathematical Foundations of Information Theory