Theorems · Theorem · functional analysis
Continuous.bounded_above_of_compact_support
∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddGroup E] [inst_1 : TopologicalSpace α] {f : α → E},
Continuous f → HasCompactSupport f → ∃ C, ∀ (x : α), ‖f x‖ ≤ C- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 157 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.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement · cited by 5,413
- Continuousstatement and proof · cited by 2,592
- HasCompactSupportstatement and proof · cited by 196
- Continuous.normproof · cited by 45
- NormedAddGroupstatement and proof · cited by 32
- HasCompactSupport.normproof · cited by 4
- Continuous.bddAbove_range_of_hasCompactSupportproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Continuous.memLp_top_of_hasCompactSupportproof · cited by 5
- MeasureTheory.integral_integral_swap_of_hasCompactSupportproof · cited by 2
- ContDiffMapSupportedIn.bounded_iteratedFDerivproof · cited by 0