KnowraProbability spaceLinked fromLinked fromThe 25 pages that link to Probability space, each with the reason it gives.All 25Broader topic 4Related 6Narrower topic 15Random variableNarrower topic: It supplies the domain and probability measure that make a random variable precise.Probability theoryBroader topic: It provides the formal setting in which probability theory assigns likelihoods.Probability distributionNarrower topic: It is the formal setting from which a random variable’s distribution is derived.Power setRelated: Its events are subsets drawn from a sigma-algebra, often contained in a power set.Probability measureBroader topic: It packages the measure with the outcomes and events on which it is defined.Conditional probabilityNarrower topic: Conditional probability modifies probabilities within this underlying model.Sigma-algebraBroader topic: Its events are precisely the sets in the space's sigma-algebra.Independence (probability theory)Narrower topic: Independence is defined for events within a probability space.Sample spaceNarrower topic: It extends the sample space by specifying events and their probabilities.Borel–Cantelli lemmaNarrower topic: The events and probabilities in the theorem live in this structure.Countable additivityRelated: Countable additivity governs probabilities of countably many disjoint events within this structure.Strong law of large numbersNarrower topic: Almost-sure convergence is defined relative to the probability measure on this space.Measure spaceBroader topic: Probability theory is measure theory with total measure normalized to one.Borel measureRelated: Borel probability measures provide the event probabilities in many topological models of randomness.Filtration (probability theory)Narrower topic: Every filtration is defined on the sigma-algebra of an underlying probability space.Linearity of expectationRelated: Expectation and dependence are defined relative to this underlying probability structure.Nonmeasurable setNarrower topic: Events must belong to its sigma-algebra; arbitrary subsets of outcomes need not be events.Random vectorNarrower topic: It supplies the outcomes and probability measure on which a random vector is defined.Bonferroni inequalitiesNarrower topic: The inequalities apply to events measured within a probability space.Kolmogorov's zero–one lawNarrower topic: The zero-or-one conclusion is a statement about probabilities within this structure.Lovász local lemmaNarrower topic: The lemma's events and conditional probabilities are defined within a probability space.Bertrand's ballot theoremRelated: The formula assumes all distinct candidate-vote sequences have equal probability.Cardinality of the continuumRelated: Continuous probability models often use sample spaces with continuum cardinality.Boole's inequalityNarrower topic: The inequality applies to events within this mathematical structure.Infinite monkey theoremNarrower topic: The theorem's random text is defined within a probability space.
KnowraProbability spaceLinked fromLinked fromThe 25 pages that link to Probability space, each with the reason it gives.All 25Broader topic 4Related 6Narrower topic 15Random variableNarrower topic: It supplies the domain and probability measure that make a random variable precise.Probability theoryBroader topic: It provides the formal setting in which probability theory assigns likelihoods.Probability distributionNarrower topic: It is the formal setting from which a random variable’s distribution is derived.Power setRelated: Its events are subsets drawn from a sigma-algebra, often contained in a power set.Probability measureBroader topic: It packages the measure with the outcomes and events on which it is defined.Conditional probabilityNarrower topic: Conditional probability modifies probabilities within this underlying model.Sigma-algebraBroader topic: Its events are precisely the sets in the space's sigma-algebra.Independence (probability theory)Narrower topic: Independence is defined for events within a probability space.Sample spaceNarrower topic: It extends the sample space by specifying events and their probabilities.Borel–Cantelli lemmaNarrower topic: The events and probabilities in the theorem live in this structure.Countable additivityRelated: Countable additivity governs probabilities of countably many disjoint events within this structure.Strong law of large numbersNarrower topic: Almost-sure convergence is defined relative to the probability measure on this space.Measure spaceBroader topic: Probability theory is measure theory with total measure normalized to one.Borel measureRelated: Borel probability measures provide the event probabilities in many topological models of randomness.Filtration (probability theory)Narrower topic: Every filtration is defined on the sigma-algebra of an underlying probability space.Linearity of expectationRelated: Expectation and dependence are defined relative to this underlying probability structure.Nonmeasurable setNarrower topic: Events must belong to its sigma-algebra; arbitrary subsets of outcomes need not be events.Random vectorNarrower topic: It supplies the outcomes and probability measure on which a random vector is defined.Bonferroni inequalitiesNarrower topic: The inequalities apply to events measured within a probability space.Kolmogorov's zero–one lawNarrower topic: The zero-or-one conclusion is a statement about probabilities within this structure.Lovász local lemmaNarrower topic: The lemma's events and conditional probabilities are defined within a probability space.Bertrand's ballot theoremRelated: The formula assumes all distinct candidate-vote sequences have equal probability.Cardinality of the continuumRelated: Continuous probability models often use sample spaces with continuum cardinality.Boole's inequalityNarrower topic: The inequality applies to events within this mathematical structure.Infinite monkey theoremNarrower topic: The theorem's random text is defined within a probability space.