Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:theorem
|
| gptkbp:appliesTo |
independent random variables
tail events |
| gptkbp:description |
events in probability theory
|
| gptkbp:has_a_focus_on |
mathematical finance
|
| https://www.w3.org/2000/01/rdf-schema#label |
Kolmogorov's zero-one law
|
| gptkbp:influences |
the study of chaos theory
|
| gptkbp:is_a |
functional analysis
real-valued functions a measure-theoretic result |
| gptkbp:is_a_platform_for |
ergodic theory
probabilistic analysis probabilistic modeling probability spaces |
| gptkbp:is_a_subject_of |
probability theory
mathematical research applied mathematics advanced probability courses theory of stochastic processes probabilistic limit theorems quantum_mechanics |
| gptkbp:is_a_tool_for |
computer science
|
| gptkbp:is_essential_for |
data analysis
stochastic processes theoretical statistics |
| gptkbp:is_featured_in |
examples from real life
|
| gptkbp:is_referenced_in |
academic papers
|
| gptkbp:is_studied_in |
convergence of random variables
|
| gptkbp:is_used_in |
machine learning
research papers mathematical literature statistical mechanics measure theory financial mathematics probability textbooks other theorems in probability |
| gptkbp:isConnectedTo |
random processes
|
| gptkbp:legal_principle |
understanding randomness
mathematical_statistics |
| gptkbp:previousName |
gptkb:Andrey_Kolmogorov
|
| gptkbp:publishedBy |
1933
|
| gptkbp:related_to |
information theory
conditional probability law of large numbers random variable distributions Borel_sets |
| gptkbp:state |
certain events have a probability of either 0 or 1
|
| gptkbp:suitableFor |
game theory
random walks |
| gptkbp:was_a_result_of |
measure-theoretic probability
the Borel-Cantelli lemma |