Robbins lemma
E1015499
Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Robbins lemma canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13012659 — 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: Robbins lemma Context triple: [Herbert Robbins, knownFor, Robbins lemma]
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A.
Bailey lemma
The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
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B.
Tucker’s lemma
Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
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C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
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D.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
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E.
Beppo Levi's lemma
Beppo Levi's lemma, also known as the monotone convergence theorem, is a fundamental result in measure theory that guarantees the convergence of integrals for non-decreasing sequences of non-negative measurable functions.
- 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: Robbins lemma Target entity description: Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
-
A.
Bailey lemma
The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
-
B.
Tucker’s lemma
Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
-
C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
D.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
-
E.
Beppo Levi's lemma
Beppo Levi's lemma, also known as the monotone convergence theorem, is a fundamental result in measure theory that guarantees the convergence of integrals for non-decreasing sequences of non-negative measurable functions.
- F. None of above. chosen
Statements (17)
| Predicate | Object |
|---|---|
| instanceOf |
lemma in probability theory
ⓘ
mathematician ⓘ |
| appliesTo | independent random variables ⓘ |
| concerns | expected maximum of partial sums of independent random variables ⓘ |
| describes | bound on the expected maximum of partial sums ⓘ |
| field |
probability theory
ⓘ
probability theory ⓘ |
| hasUse |
analysis of random processes
ⓘ
bounding tail behavior of sums of random variables ⓘ deriving inequalities in probability ⓘ |
| knownFor | Robbins lemma NERFINISHED ⓘ |
| namedAfter |
American mathematician Herbert Robbins
NERFINISHED
ⓘ
Herbert Robbins NERFINISHED ⓘ |
| relatedTo |
concentration inequalities
ⓘ
laws of large numbers ⓘ martingale inequalities ⓘ maximal inequalities in probability ⓘ |
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: Robbins lemma Description of subject: Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.