definition 11.38 Measure-preserving map; invariant measure; ergodicity

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:978 · p. 382

Rests on

depends_on definition 11.34 Measure; measure space ¶
- depends_on definition 11.1 Discrete probability space ¶
  - depends_on definition 7.45 Series ¶
    - depends_on definition 7.2 Absolute value ¶
    - depends_on definition 7.4 Convergence ¶
      - depends_on definition 7.2 Absolute value ¶ ↺
- depends_on definition 11.33 Sigma-algebra ¶
  - depends_on definition 11.1 Discrete probability space ¶ ↺
  - depends_on definition 6.1 Topological space ¶
    - depends_on definition 3.31 Empty set ¶
    - depends_on definition 3.35 Union, intersection, difference ¶
      - depends_on definition 3.8 Conjunction ¶
      - depends_on definition 3.9 Disjunction ¶
      - depends_on definition 3.7 Negation ¶
    - depends_on definition 3.30 Subset ¶
    - depends_on equation 3.51 eq:set-indexed ¶
depends_on definition 11.35 Null set; almost everywhere ¶
- depends_on definition 11.34 Measure; measure space ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Measure; measure space	declared	parts/02-mathematical-methods/09-probability-statistics.tex:995
`depends_on`	→	Null set; almost everywhere	declared	parts/02-mathematical-methods/09-probability-statistics.tex:995
`depends_on`	←	Birkhoff's pointwise ergodic theorem	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1013