Theorems · Theorem · real analysis
eVariationOn_id
∀ {a b : ℝ} {s : Set ℝ}, a ∈ s → b ∈ s → eVariationOn id (s ∩ Set.Icc a b) = ENNReal.ofReal (b - a)The variation of the identity on s ∩ Icc a b is b - a.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Set.Iccstatement · cited by 1,702
- ENNReal.ofRealstatement · cited by 863
- eVariationOnstatement · cited by 90
- Monotone.monotoneOnproof · cited by 43
- monotone_idproof · cited by 31
- MonotoneOn.eVariationOn_eqproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- eVariationOn_id_Iccproof · cited by 1