Theorems · Definition · convex and discrete geometry
Convexity.StdSimplex.single
{R : Type u} →
[inst : PartialOrder R] →
[inst_1 : Semiring R] → {M : Type u_9} → [IsStrictOrderedRing R] → M → Convexity.StdSimplex R MThe point mass distribution concentrated at x.
- Defined in
- Mathlib.Geometry.Convex.ConvexSpace.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Finsupp.singleproof · cited by 943
- Convexity.StdSimplexstatement · cited by 123
Cited by25
Results whose statement or proof uses this declaration.
- Convexity.ConvexSpace.sConvexComb_singlestatement · cited by 9
- Convexity.StdSimplex.weights_singlestatement and proof · cited by 5
- Convexity.StdSimplex.map_conststatement · cited by 4
- Convexity.convexCombPair_sameproof · cited by 2
- Convexity.StdSimplex.map_singlestatement and proof · cited by 1
- Convexity.StdSimplex.restrict_singletonstatement · cited by 1
- Convexity.StdSimplex.single.congr_simpstatement and proof · cited by 1
- Convexity.IsConvexSet.singletonproof · cited by 1
- Convexity.convexCombPair_convexCombPair_assoc_leftproof · cited by 1
- Convexity.convexCombPair_convexCombPair_left_eq_sConvexCombstatement and proof · cited by 1
- Convexity.convexCombPair_convexCombPair_right_eq_sConvexCombstatement and proof · cited by 1
- Convexity.convexCombPair_iConvexComb_leftstatement and proof · cited by 1