lemma A.247 Integration against a projection-valued measure

Rests on

• depends_on definition 12.58 Projection-valued measure ¶
  • depends_on definition 12.41 The operator classes ¶
    • 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 ¶
    • depends_on proposition 12.21 Characterization of orthogonal projections ¶
      • depends_on definition 12.20 Orthogonal projection operator ¶
        • depends_on theorem 12.18 Projection theorem ¶
      • depends_on theorem 12.18 Projection theorem ¶ ↺
      • proves proof ch:10-hilbert-spaces@proof-11 ¶
    • depends_on theorem 12.38 Existence and uniqueness of the adjoint ¶
      • depends_on definition 5.41 Adjoint ¶
        • depends_on definition 5.18 Inner product ¶
        • depends_on definition 5.37 Linear transformation ¶
      • depends_on proposition 12.37 $\mathcal{B}(\mathcal{H})$ is a Banach algebra ¶
        • depends_on definition 12.35 Bounded operator; operator norm ¶
        • depends_on proposition 12.8 Absolutely convergent series test ¶
        • proves proof ch:10-hilbert-spaces@proof-19 ¶
      • depends_on theorem 12.46 Riesz representation ¶
        • depends_on definition 12.45 Continuous linear functional; the dual ¶
        • depends_on theorem 12.18 Projection theorem ¶ ↺
        • proves proof ch:10-hilbert-spaces@proof-24 ¶
      • proves proof ch:10-hilbert-spaces@proof-20 ¶
  • depends_on proposition 12.21 Characterization of orthogonal projections ¶ ↺
• depends_on theorem 12.46 Riesz representation ¶ ↺
• proves proof app:A-long-proofs@proof-152 ¶

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