proposition A.142 The mollification is smooth

Rests on

• depends_on lemma A.136 Differentiation under the integral sign ¶
  • 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 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 7.97 Partial derivative; gradient ¶
      • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on definition 7.16 Limit ¶ ↺
        • depends_on definition 7.9 Real function ¶ ↺
      • depends_on definition 5.15 Basis ¶
        • depends_on definition 5.12 Subspace generated by a set of vectors ¶
        • depends_on definition 5.14 Linear independence ¶
  • depends_on theorem 6.11 Heine–Borel on $\R$ ¶
    • depends_on axiom 7.1 Completeness of $\R$ ¶
    • depends_on definition 6.9 Compact set ¶
      • depends_on definition 6.5 Open cover ¶
        • depends_on definition 6.2 Open set ¶
        • depends_on equation 3.51 eq:set-indexed ¶
    • proves proof ch:04-topology@proof-2 ¶
  • proves proof app:A-long-proofs@proof-83 ¶
• 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 ¶
      • depends_on definition 7.98 Functions of class $C^{1}$ ¶ ↺
      • 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 lemma A.138 The flat exponential ¶ ↺
  • proves proof app:A-long-proofs@proof-85 ¶
• proves proof app:A-long-proofs@proof-86 ¶

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