lemma A.196 Inversion for a difference

open in the book · appendices/A-long-proofs.tex:9979 · p. 2887

Rests on

depends_on lemma A.195 Riemann–Lebesgue, continuous compactly supported case ¶
- depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
  - depends_on proposition 7.22 Sequential characterization ¶
    - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on equation 7.7 eq:ana-limit-left ¶
      - depends_on equation 7.5 eq:ana-limit-right ¶
    - depends_on definition 7.4 Convergence ¶
      - depends_on definition 7.2 Absolute value ¶
    - proves proof ch:05-real-analysis@proof-7 ¶
  - depends_on theorem 7.7 Bolzano–Weierstrass ¶
    - depends_on corollary A.45 Archimedean property and density of $\Q$ ¶
      - depends_on definition A.36 Cut ¶
      - depends_on theorem A.40 Least-upper-bound property ¶
      - proves proof app:A-long-proofs@proof-32 ¶
    - depends_on corollary A.46 Monotone convergence ¶
      - depends_on theorem A.40 Least-upper-bound property ¶ ↺
      - proves proof app:A-long-proofs@proof-33 ¶
    - proves proof ch:05-real-analysis@proof-4 ¶
  - proves proof ch:05-real-analysis@proof-10 ¶
- proves proof app:A-long-proofs@proof-119 ¶
depends_on theorem A.177 Fourier inversion for a distribution function ¶
- 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 definition 7.26 Derivative of a function at a point ¶
    - 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 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 ¶
proves proof app:A-long-proofs@proof-120 ¶

Supports

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`	→	Riemann–Lebesgue, continuous compactly supported case	declared	appendices/A-long-proofs.tex:9991
`depends_on`	→	Fourier inversion for a distribution function	declared	appendices/A-long-proofs.tex:9991
`depends_on`	←	Esseen's smoothing inequality	declared	appendices/A-long-proofs.tex:10053
`proves`	←	app:A-long-proofs@proof-120	declared	appendices/A-long-proofs.tex:9994