LLN
E582381
LLN is a fundamental theorem in probability theory stating that as the number of independent, identically distributed trials increases, the sample average converges to the expected value.
All labels observed (1)
| Label | Occurrences |
|---|---|
| LLN canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6293642 — 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: LLN Context triple: [law of large numbers, alsoKnownAs, LLN]
-
A.
NNL
NNL is the commonly used abbreviation for the Negro National League, a pioneering professional baseball league that was a cornerstone of Negro league baseball in the early 20th century.
-
B.
LL
LL is the German vehicle registration code assigned to the district of Landsberg am Lech in Bavaria.
-
C.
NLL
The NLL (National Lacrosse League) is North America’s premier professional indoor box lacrosse league.
-
D.
LN
LN is the postcode area designation for Lincoln and its surrounding region in the United Kingdom.
-
E.
LN1
LN1 is the first French high-speed rail line (LGV Sud-Est), connecting Paris to Lyon and pioneering the TGV network.
- 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: LLN Target entity description: LLN is a fundamental theorem in probability theory stating that as the number of independent, identically distributed trials increases, the sample average converges to the expected value.
-
A.
NNL
NNL is the commonly used abbreviation for the Negro National League, a pioneering professional baseball league that was a cornerstone of Negro league baseball in the early 20th century.
-
B.
LL
LL is the German vehicle registration code assigned to the district of Landsberg am Lech in Bavaria.
-
C.
NLL
The NLL (National Lacrosse League) is North America’s premier professional indoor box lacrosse league.
-
D.
LN
LN is the postcode area designation for Lincoln and its surrounding region in the United Kingdom.
-
E.
LN1
LN1 is the first French high-speed rail line (LGV Sud-Est), connecting Paris to Lyon and pioneering the TGV network.
- F. None of above. chosen
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf |
law of large numbers
ⓘ
probability theorem ⓘ |
| alsoKnownAs |
strong law of large numbers
ⓘ
weak law of large numbers ⓘ |
| appliesTo | independent identically distributed random variables ⓘ |
| assumes |
finite expected value
ⓘ
identical distribution of trials ⓘ independence of trials ⓘ |
| category | limit theorem in probability ⓘ |
| contrastedWith | central limit theorem ⓘ |
| describes | convergence of sample averages to expected value ⓘ |
| ensures | stability of long-run frequencies ⓘ |
| field |
probability theory
ⓘ
statistics ⓘ |
| formalization | measure-theoretic probability framework ⓘ |
| formalizes | long-run average behavior of random experiments ⓘ |
| fullName | law of large numbers ⓘ |
| hasConsequence | empirical mean is consistent estimator of expectation ⓘ |
| hasVariant |
strong law of large numbers
ⓘ
weak law of large numbers ⓘ
linked to:
law of large numbers
|
| historicalOrigin | Jakob Bernoulli ⓘ |
| holdsUnder | certain moment conditions ⓘ |
| implies |
law of averages in colloquial terms
ⓘ
sample mean approximates population mean ⓘ |
| mathematicalObject | theorem about sequences of random variables ⓘ |
| motivates | use of sample averages in statistics ⓘ |
| provenBy |
Chebyshev
ⓘ
Kolmogorov ⓘ
linked to:
Andrei Kolmogorov
|
| relatedConcept |
Borel–Cantelli lemma
ⓘ
linked to:
Borel–Cantelli lemmas
Chebyshev inequality ⓘ
linked to:
Chebyshev inequalities
ergodic theorem ⓘ |
| requires | large number of trials ⓘ |
| typeOfConvergence |
almost sure convergence
ⓘ
convergence in probability ⓘ |
| usedIn |
Monte Carlo methods
ⓘ
frequentist interpretation of probability ⓘ statistical inference ⓘ |
| yearFirstFormulated | early 18th century ⓘ |
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: LLN Description of subject: LLN is a fundamental theorem in probability theory stating that as the number of independent, identically distributed trials increases, the sample average converges to the expected value.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.