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A measure space with total mass one.
wp-probabilitynlab-probability-spacetao-measure-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Restrict to measures with ; this is a property, not an instruction to rescale an arbitrary measure.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-probabilitytao-measure-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
For an event with , restricting to intersections with and dividing by gives the conditional probability measure.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-conditional-probabilitynlab-probability-theorydurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the Probability space structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-filtered-probabilitydurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the probability measure and its underlying measurable space.
Feed several structures into a construction junction and impose compatibility between them.
wp-random-variabledurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
Require a standard Borel realization modulo null sets.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-standard-probabilitydurrett-probability