theorem A.223 Tonelli and dominated convergence, as used here

open in the book · appendices/A-long-proofs.tex:11288 · p. 2900

Rests on

depends_on definition 11.4 Expectation ¶
- 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 11.3 Discrete random variable ¶
  - depends_on definition 11.1 Discrete probability space ¶
    - depends_on definition 7.45 Series ¶ ↺

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type	direction	node	provenance	where
`cites`	→	Probability and Measure	derived	appendices/A-long-proofs.tex:11301
`depends_on`	→	Expectation	declared	appendices/A-long-proofs.tex:11302