proposition A.143 Reproduction identity

Rests on

• depends_on definition A.141 Mollification ¶
  • 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 7.97 Partial derivative; gradient ¶
      • depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
        • depends_on proposition 7.30 Leibniz rule ¶
        • depends_on theorem 7.34 Rolle ¶
        • proves proof ch:05-real-analysis@proof-22 ¶
      • proves proof app:A-long-proofs@proof-84 ¶
  • depends_on definition 6.2 Open set ¶
    • depends_on definition 6.1 Topological space ¶
      • depends_on definition 3.31 Empty set ¶
      • depends_on definition 3.35 Union, intersection, difference ¶
        • depends_on definition 3.8 Conjunction ¶
        • depends_on definition 3.9 Disjunction ¶
        • depends_on definition 3.7 Negation ¶
      • depends_on definition 3.30 Subset ¶
      • depends_on equation 3.51 eq:set-indexed ¶
• depends_on definition A.134 Mean-value property ¶
  • depends_on definition 6.2 Open set ¶ ↺
  • depends_on equation 10.54 eq:pde-spherical-mean ¶
• depends_on lemma A.140 Properties of the mollifier ¶
  • depends_on definition A.139 The standard radial mollifier ¶ ↺
  • depends_on lemma A.138 The flat exponential ¶ ↺
  • proves proof app:A-long-proofs@proof-85 ¶
• proves proof app:A-long-proofs@proof-87 ¶

Supports

Nothing declares a dependency on this node yet.