definition A.498 Zero content
open in the book ·
appendices/A-long-proofs.tex:24457
· p. 3037
- ground object -- no derivation owed
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 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
definition 6.1
Topological space
¶
- depends_on equation 3.51 eq:set-indexed ¶ ↺
-
depends_on
definition 6.2
Open set
¶
-
depends_on
definition 6.5
Open cover
¶
Supports
-
depends_on
lemma A.499
What zero content buys
¶
- depends_on corollary A.514 Degeneracy on a negligible set ¶
-
depends_on
lemma A.500
Graphs and $C^{1}$ images have zero content
¶
- depends_on corollary A.514 Degeneracy on a negligible set ¶ ↺
-
depends_on
lemma A.512
The boundary strip is thin
¶
-
depends_on
theorem A.513
Change of variables
¶
- depends_on corollary A.514 Degeneracy on a negligible set ¶ ↺
- depends_on remark A.516 The hypotheses of the global form ¶
-
depends_on
theorem A.513
Change of variables
¶
- depends_on theorem A.513 Change of variables ¶ ↺
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 |
→ | Multiple integral | declared | appendices/A-long-proofs.tex:24462 |
depends_on |
→ | Compact set | declared | appendices/A-long-proofs.tex:24462 |
depends_on |
← | What zero content buys | declared | appendices/A-long-proofs.tex:24487 |