theorem A.244 Riesz–Markov; quoted

open in the book · appendices/A-long-proofs.tex:12163 · p. 2910

Rests on

depends_on definition 6.9 Compact set ¶
- depends_on definition 6.5 Open cover ¶
  - 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 3.30 Subset ¶
      - depends_on equation 3.51 eq:set-indexed ¶
  - depends_on equation 3.51 eq:set-indexed ¶ ↺

Supports

depends_on lemma A.249 The cyclic case ¶
depends_on proposition A.245 The measures $\mu_{x,y}$ ¶
- depends_on lemma A.249 The cyclic case ¶ ↺
- depends_on proposition A.246 Bounded Borel functional calculus ¶
  - depends_on proposition A.262 Spectral theorem for an unbounded self-adjoint operator ¶
    - depends_on proposition A.280 Direct-integral form of the spectral theorem ¶
      - depends_on proposition A.282 The fibre maps are continuous on $\Phi$ ¶
  - depends_on proposition A.261 Spectral theorem for a unitary operator ¶
    - depends_on proposition A.262 Spectral theorem for an unbounded self-adjoint operator ¶ ↺

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`	→	Compact set	declared	appendices/A-long-proofs.tex:12175
`depends_on`	←	The cyclic case	declared	appendices/A-long-proofs.tex:12441
`depends_on`	←	The measures $\mu_{x,y}$	declared	appendices/A-long-proofs.tex:12191