theorem A.206 Cramér–Wold, and continuous mapping

open in the book · appendices/A-long-proofs.tex:10473 · p. 2892

Rests on

depends_on definition 11.21 Distribution function ¶
- depends_on definition 11.20 Density ¶
  - depends_on definition 7.39 Darboux sums and the definite integral ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶
depends_on lemma 11.52 Slutsky ¶
- depends_on definition 11.21 Distribution function ¶ ↺
- proves proof ch:09-probability-statistics@proof-20 ¶
- proves proof ch:09-probability-statistics@proof-21 ¶

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 ¶ ↺
depends_on theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`cites`	→	Probability and Measure	derived	appendices/A-long-proofs.tex:10482
`depends_on`	→	Distribution function	declared	appendices/A-long-proofs.tex:10483
`depends_on`	→	Slutsky	declared	appendices/A-long-proofs.tex:10483
`depends_on`	←	The three averages	declared	appendices/A-long-proofs.tex:10514
`depends_on`	←	Wilks, $k$ parameters and $r$ constraints	declared	appendices/A-long-proofs.tex:10914