theorem A.205 Weak law under integrability alone

open in the book · appendices/A-long-proofs.tex:10464 · p. 2892

Rests on

depends_on corollary 11.51 Weak law of large numbers ¶
- depends_on lemma 11.50 Markov and Chebyshev inequalities ¶
  - depends_on definition 11.6 Moments, variance, standard deviation ¶
    - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶
      - depends_on definition 11.4 Expectation ¶
      - depends_on proposition 11.2 Elementary rules ¶
      - proves proof ch:09-probability-statistics@proof-2 ¶
  - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
  - proves proof ch:09-probability-statistics@proof-18 ¶
- proves proof ch:09-probability-statistics@proof-19 ¶

Supports

depends_on lemma A.208 The three averages ¶
- depends_on corollary A.210 Uniform quadratic approximation on the $n^{-1/2}$ scale ¶
  - depends_on lemma A.213 The three minima ¶
    - depends_on theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶
- depends_on lemma A.211 Root-$n$ localisation ¶
  - depends_on lemma A.213 The three minima ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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partly declared
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Edges

type	direction	node	provenance	where
`cites`	→	Probability and Measure	derived	appendices/A-long-proofs.tex:10469
`depends_on`	→	Weak law of large numbers	declared	appendices/A-long-proofs.tex:10470
`depends_on`	←	The three averages	declared	appendices/A-long-proofs.tex:10514