Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
A set equipped with a -algebra of measurable subsets.
wp-measurablenlab-measurable-spacetao-measure-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Retain only the Borel -algebra as a measurable-space structure.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-borelwp-measurabletao-measure-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Choose measurable subsets.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-measurabletao-measure-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Supply the measurable space whose sub--algebras form the filtration.
Feed several structures into a construction junction and impose compatibility between them.
wp-filtration-probabilitydurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
Instantiate measurable-space structure on both domain and codomain.
Feed several structures into a construction junction and impose compatibility between them.
wp-measurable-functiontao-measure-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Choose a countably additive measure.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-measure-spacetao-measure-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
A POVM adds a normalized, weakly countably additive assignment of a positive operator to each measurable outcome set.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-positive_operatornlab-positive_operatortong-quantumwp-positive_operator_valued_measurenlab-positive_operator_valued_measurenist-quantum-theory