definition A.304 Integral over a chart

open in the book · appendices/A-long-proofs.tex:15020 · p. 2940

Rests on

depends_on definition 7.125 Multiple integral ¶
- depends_on axiom 7.1 Completeness of $\R$ ¶
- depends_on definition 7.39 Darboux sums and the definite integral ¶
  - depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
depends_on definition A.302 Orientation ¶
- depends_on definition 13.44 Atlas ¶
  - depends_on definition 13.43 Coordinate system ¶
- depends_on lemma A.301 Transformation of the top form ¶
  - depends_on definition 13.102 Wedge product ¶
    - depends_on definition 13.98 $k$-form ¶
      - depends_on definition 13.83 Covector ¶
      - depends_on definition 13.84 Tensor ¶
    - depends_on equation 13.239 eq:mfd-dual-basis ¶
  - depends_on equation 13.241 eq:mfd-antisimb ¶
  - depends_on proposition 13.100 The space of $k$-forms ¶
    - depends_on definition 13.83 Covector ¶ ↺
    - depends_on definition 13.98 $k$-form ¶ ↺
    - depends_on definition 13.84 Tensor ¶ ↺
    - proves proof ch:11-manifolds-tensors-curvature@proof-20 ¶
  - proves proof app:A-long-proofs@proof-189 ¶
depends_on proposition 13.100 The space of $k$-forms ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Multiple integral	declared	appendices/A-long-proofs.tex:15032
`depends_on`	→	Orientation	declared	appendices/A-long-proofs.tex:15032
`depends_on`	→	The space of $k$-forms	declared	appendices/A-long-proofs.tex:15032
`depends_on`	←	The chart integral is well defined	declared	appendices/A-long-proofs.tex:15040