theorem 11.39 Birkhoff's pointwise ergodic theorem

Rests on

• depends_on definition 11.38 Measure-preserving map; invariant measure; ergodicity ¶
  • 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 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 3.30 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 ¶ ↺
• depends_on proposition 11.36 Monotonicity, countable subadditivity, and null sets ¶
  • depends_on definition 11.34 Measure; measure space ¶ ↺
  • depends_on definition 11.35 Null set; almost everywhere ¶ ↺
  • proves proof ch:09-probability-statistics@proof-14 ¶

Supports

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