lemma A.140 Properties of the mollifier

open in the book · appendices/A-long-proofs.tex:7729 · p. 2862

Rests on

depends_on definition A.139 The standard radial mollifier ¶
- depends_on lemma A.138 The flat exponential ¶
  - depends_on definition 7.98 Functions of class $C^{1}$ ¶
    - 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 7.97 Partial derivative; gradient ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 5.15 Basis ¶
  - depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
    - depends_on proposition 7.30 Leibniz rule ¶
      - depends_on definition 7.12 Product of functions ¶
      - depends_on equation 7.14 eq:ana-derivh ¶
      - depends_on proposition 7.27 Differentiable implies continuous ¶
      - depends_on proposition 7.6 Algebra of limits ¶
      - proves proof ch:05-real-analysis@proof-14 ¶
    - depends_on theorem 7.34 Rolle ¶
      - depends_on lemma 7.33 Fermat: interior extremum ¶
      - depends_on theorem 7.24 Extreme value theorem ¶
      - proves proof ch:05-real-analysis@proof-18 ¶
    - proves proof ch:05-real-analysis@proof-22 ¶
  - proves proof app:A-long-proofs@proof-84 ¶
depends_on lemma A.138 The flat exponential ¶ ↺
proves proof app:A-long-proofs@proof-85 ¶

Supports

depends_on proposition A.143 Reproduction identity ¶
depends_on proposition A.142 The mollification is smooth ¶

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`	→	The standard radial mollifier	declared	appendices/A-long-proofs.tex:7735
`depends_on`	→	The flat exponential	declared	appendices/A-long-proofs.tex:7735
`depends_on`	←	Reproduction identity	declared	appendices/A-long-proofs.tex:7850
`depends_on`	←	The mollification is smooth	declared	appendices/A-long-proofs.tex:7794
`proves`	←	app:A-long-proofs@proof-85	declared	appendices/A-long-proofs.tex:7739