lemma A.195 Riemann–Lebesgue, continuous compactly supported case

open in the book · appendices/A-long-proofs.tex:9951 · p. 2886

Rests on

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 definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - 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 ¶
      - depends_on definition A.36 Cut ¶ ↺
      - depends_on definition A.38 Order on $\R$ ¶
      - proves proof app:A-long-proofs@proof-29 ¶
    - 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 ¶

Supports

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`	→	Heine–Cantor: uniform continuity	declared	appendices/A-long-proofs.tex:9956
`depends_on`	←	Inversion for a difference	declared	appendices/A-long-proofs.tex:9991
`proves`	←	app:A-long-proofs@proof-119	declared	appendices/A-long-proofs.tex:9959