theorem A.177 Fourier inversion for a distribution function

open in the book · appendices/A-long-proofs.tex:9178 · p. 2877

Rests on

depends_on definition 11.42 Characteristic function ¶
depends_on lemma A.172 Dirichlet ¶
- depends_on equation 7.28 eq:ana-parts ¶
- depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
  - depends_on definition 7.41 Antiderivative ¶
    - depends_on corollary 7.36 cor:ana-mvt-consequences ¶
      - depends_on theorem 7.35 Mean value theorem ¶
      - proves proof ch:05-real-analysis@proof-20 ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
  - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
    - depends_on theorem 7.40 Continuous functions are integrable ¶
      - depends_on definition 7.39 Darboux sums and the definite integral ¶
      - depends_on theorem 7.24 Extreme value theorem ¶
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      - proves proof ch:05-real-analysis@proof-23 ¶
    - depends_on theorem 7.24 Extreme value theorem ¶ ↺
    - proves proof ch:05-real-analysis@proof-24 ¶
  - proves proof ch:05-real-analysis@proof-25 ¶
- proves proof app:A-long-proofs@proof-100 ¶
proves proof app:A-long-proofs@proof-104 ¶

Supports

depends_on corollary A.178 The characteristic function determines the distribution ¶
- depends_on lemma A.220 At each point, field and derivative are independent Gaussians ¶
depends_on lemma A.196 Inversion for a difference ¶
- depends_on theorem A.198 Esseen's smoothing inequality ¶

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
`depends_on`	→	Characteristic function	declared	appendices/A-long-proofs.tex:9190
`depends_on`	→	Dirichlet	declared	appendices/A-long-proofs.tex:9190
`depends_on`	←	The characteristic function determines the distribution	declared	appendices/A-long-proofs.tex:9240
`depends_on`	←	Inversion for a difference	declared	appendices/A-long-proofs.tex:9991
`proves`	←	app:A-long-proofs@proof-104	declared	appendices/A-long-proofs.tex:9193