definition 7.138 Set of measure zero

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:4716 · p. 261

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 3.65 Countable set ¶
- depends_on axiom 3.33 Peano axioms ¶
- depends_on definition 3.62 Equipotence ¶
  - depends_on definition 3.47 Bijective map ¶
  - depends_on definition 3.40 Cardinal ¶

Supports

depends_on definition 7.140 Hausdorff measure ¶
- depends_on definition 7.142 Box-counting dimension ¶
  - depends_on definition 32.79 Box-counting dimension, restated from Part II ¶
    - depends_on definition 32.81 Correlation dimension ¶
    - depends_on example 32.80 The middle-thirds Cantor set ¶
  - depends_on proposition 7.143 The Hausdorff dimension never exceeds the box dimension ¶
  - depends_on remark 7.144 What is developed here, and what is not ¶
- depends_on proposition 7.141 The critical exponent, and the Hausdorff dimension ¶
  - depends_on proposition 7.143 The Hausdorff dimension never exceeds the box dimension ¶ ↺
- depends_on remark 7.144 What is developed here, and what is not ¶ ↺
depends_on lemma 7.139 A countable union of null sets is null ¶
- depends_on proposition 7.143 The Hausdorff dimension never exceeds the box dimension ¶ ↺
- depends_on proposition 7.141 The critical exponent, and the Hausdorff dimension ¶ ↺
- depends_on remark 7.94 Three numbers, two kinds ¶
depends_on proposition 7.141 The critical exponent, and the Hausdorff dimension ¶ ↺
depends_on remark 7.144 What is developed here, and what is not ¶ ↺

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	parts/02-mathematical-methods/05-real-analysis.tex:4725
`depends_on`	→	Countable set	declared	parts/02-mathematical-methods/05-real-analysis.tex:4725
`depends_on`	←	Hausdorff measure	declared	parts/02-mathematical-methods/05-real-analysis.tex:4775
`depends_on`	←	A countable union of null sets is null	declared	parts/02-mathematical-methods/05-real-analysis.tex:4733
`depends_on`	←	The critical exponent, and the Hausdorff dimension	declared	parts/02-mathematical-methods/05-real-analysis.tex:4792
`depends_on`	←	What is developed here, and what is not	declared	parts/02-mathematical-methods/05-real-analysis.tex:4939