proposition 11.22 Properties of the distribution function

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:595 · p. 377

Rests on

depends_on definition 11.21 Distribution function ¶
- depends_on definition 11.20 Density ¶
  - depends_on definition 7.39 Darboux sums and the definite integral ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶
depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
- depends_on definition 7.26 Derivative of a function at a point ¶
  - depends_on definition 7.16 Limit ¶
    - depends_on definition 7.2 Absolute value ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - depends_on definition 7.9 Real function ¶ ↺
- depends_on theorem 7.40 Continuous functions are integrable ¶
  - depends_on definition 7.39 Darboux sums and the definite integral ¶ ↺
  - depends_on theorem 7.24 Extreme value theorem ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
    - depends_on proposition 7.22 Sequential characterization ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.4 Convergence ¶
      - proves proof ch:05-real-analysis@proof-7 ¶
    - depends_on theorem 7.7 Bolzano–Weierstrass ¶
      - depends_on corollary A.45 Archimedean property and density of $\Q$ ¶
      - depends_on corollary A.46 Monotone convergence ¶
      - proves proof ch:05-real-analysis@proof-4 ¶
    - proves proof ch:05-real-analysis@proof-9 ¶
  - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
    - depends_on proposition 7.22 Sequential characterization ¶ ↺
    - depends_on theorem 7.7 Bolzano–Weierstrass ¶ ↺
    - proves proof ch:05-real-analysis@proof-10 ¶
  - proves proof ch:05-real-analysis@proof-23 ¶
- depends_on theorem 7.24 Extreme value theorem ¶ ↺
- proves proof ch:05-real-analysis@proof-24 ¶
proves proof ch:09-probability-statistics@proof-9 ¶

Supports

depends_on proposition 11.27 Probability integral transform ¶

Neighborhood

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Edges

type	direction	node	provenance	where
`depends_on`	→	Distribution function	declared	parts/02-mathematical-methods/09-probability-statistics.tex:602
`depends_on`	→	Fundamental theorem of calculus, I	declared	parts/02-mathematical-methods/09-probability-statistics.tex:602
`depends_on`	←	Probability integral transform	declared	parts/02-mathematical-methods/09-probability-statistics.tex:704
`proves`	←	ch:09-probability-statistics@proof-9	declared	parts/02-mathematical-methods/09-probability-statistics.tex:605