lemma A.220 At each point, field and derivative are independent Gaussians

Rests on

• depends_on corollary A.178 The characteristic function determines the distribution ¶
  • depends_on theorem A.177 Fourier inversion for a distribution function ¶
    • depends_on definition 11.42 Characteristic function ¶
    • depends_on lemma A.172 Dirichlet ¶
      • 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 theorem 7.42 Fundamental theorem of calculus, I ¶
        • proves proof ch:05-real-analysis@proof-25 ¶
      • proves proof app:A-long-proofs@proof-100 ¶
    • proves proof app:A-long-proofs@proof-104 ¶
  • proves proof app:A-long-proofs@proof-105 ¶
• depends_on definition A.218 The hypotheses ¶
  • depends_on definition 11.28 Gaussian distribution ¶
    • depends_on definition 11.20 Density ¶
      • depends_on definition 7.39 Darboux sums and the definite integral ¶
        • depends_on axiom 7.1 Completeness of $\R$ ¶
  • depends_on definition 11.100 Upcrossings ¶
    • depends_on definition 11.96 Local, global, trials factor ¶
      • depends_on definition 11.75 $p$-value ¶
        • depends_on definition 11.74 Hypotheses and tests ¶
      • depends_on equation 11.89 eq:prob-p-one-sided ¶
      • depends_on equation 11.88 eq:prob-q0 ¶
• proves proof app:A-long-proofs@proof-133 ¶

Supports

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