Limit Laws for Sums of Independent Random Variables
E379000
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T3677829 — 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: Limit Laws for Sums of Independent Random Variables Context triple: [Aleksandr Khinchin, notableWork, Limit Laws for Sums of Independent Random Variables]
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A.
Lindeberg–Feller central limit theorem
The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
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B.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
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C.
Isserlis’ theorem in probability theory
Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
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D.
Modern Probability Theory and Its Applications
"Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
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E.
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.
- 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: Limit Laws for Sums of Independent Random Variables Target entity description: Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
-
A.
Lindeberg–Feller central limit theorem
The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
-
B.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
C.
Isserlis’ theorem in probability theory
Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
-
D.
Modern Probability Theory and Its Applications
"Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
-
E.
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.
- F. None of above. chosen
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical work
ⓘ
monograph ⓘ |
| assumesKnowledgeOf |
measure-theoretic probability
ⓘ
real analysis ⓘ |
| audience |
graduate students in probability
ⓘ
researchers in probability theory ⓘ |
| contribution |
clarifies conditions for central limit behavior
ⓘ
clarifies conditions for law of large numbers ⓘ provides a unified framework for limit laws of sums ⓘ |
| field |
mathematical statistics
ⓘ
probability theory ⓘ |
| focus |
rigorous treatment of sums of independent random variables
ⓘ
systematic development of probability limit theorems ⓘ |
| importance |
foundational in the theory of probability limit theorems
ⓘ
used as a reference in advanced probability courses ⓘ |
| relatedTo |
central limit theorem
ⓘ
surface form:
classical central limit theorem
classical law of large numbers ⓘ modern probability textbooks on limit theorems ⓘ |
| structure | organized around asymptotic results for sums ⓘ |
| topic |
almost sure convergence
ⓘ
asymptotic behavior of sums ⓘ central limit behavior ⓘ central limit theorem ⓘ convergence in distribution ⓘ convergence in probability ⓘ independent random variables ⓘ law of large numbers ⓘ limit theorems ⓘ normal approximation ⓘ probability limit theorems ⓘ stability of sums ⓘ strong law of large numbers ⓘ sums of independent random variables ⓘ triangular arrays of random variables ⓘ law of large numbers ⓘ
surface form:
weak law of large numbers
|
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: Limit Laws for Sums of Independent Random Variables Description of subject: Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Random Variables and Probability Distributions
this entity surface form:
Théorie de l’addition des variables aléatoires
Soviet school of probability theory
→
notableWork
→
Limit Laws for Sums of Independent Random Variables
ⓘ
this entity surface form:
limit theorems in probability