lemma A.172 Dirichlet

open in the book · appendices/A-long-proofs.tex:8944 · p. 2875

Rests on

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 ¶
      - depends_on proposition 7.29 Linearity ¶
      - depends_on theorem 7.34 Rolle ¶
      - proves proof ch:05-real-analysis@proof-19 ¶
    - 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 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - 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 axiom 7.1 Completeness of $\R$ ¶
    - depends_on theorem 7.24 Extreme value theorem ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
      - depends_on proposition 7.22 Sequential characterization ¶
      - depends_on theorem 7.7 Bolzano–Weierstrass ¶
      - proves proof ch:05-real-analysis@proof-9 ¶
    - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      - depends_on proposition 7.22 Sequential characterization ¶ ↺
      - depends_on theorem 7.7 Bolzano–Weierstrass ¶ ↺
      - proves proof ch:05-real-analysis@proof-10 ¶
    - 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 ¶

Supports

depends_on lemma A.193 A cosine integral ¶
- depends_on lemma A.194 The Fejér kernel and its transform ¶
  - depends_on theorem A.198 Esseen's smoothing inequality ¶
depends_on theorem A.177 Fourier inversion for a distribution function ¶
- 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.

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partly declared
a check failed
not graded
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inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:ana-parts	declared	appendices/A-long-proofs.tex:8958
`depends_on`	→	Fundamental theorem of calculus, II	declared	appendices/A-long-proofs.tex:8958
`depends_on`	←	A cosine integral	declared	appendices/A-long-proofs.tex:9862
`depends_on`	←	Fourier inversion for a distribution function	declared	appendices/A-long-proofs.tex:9190
`proves`	←	app:A-long-proofs@proof-100	declared	appendices/A-long-proofs.tex:8961