Order, lattices, ordered algebraic structures Binary relations and basic order notions Concept
Infimum
Summary
The infimum of a set is its greatest lower bound. It is a lower bound of the set that is greater than or equal to every other lower bound. It is the dual notion of the supremum.
Where this leads
55 pages build on this one.
- Jordan measure
- Stokes' theorem
- Surface integral
- Orientable surface
- Cavalieri's principle
- Generalised Stokes theorem
- Divergence theorem
- Volume of a box
- Volume of a ball in R^3
- Surface area
- Flux through a surface
- Homotopy invariance of line integrals of closed forms
- Shell theorem
- Cheng–Yau gradient estimate
- Removable singularities for harmonic functions
- Harmonic majorant
- Hausdorff measure
- Conditionally complete lattice
- Smoothness and analyticity of harmonic functions
- Varadhan's lemma
- Sub-mean value property
- Robust statistics
- Hausdorff distance
- Injectivity radius
- Join and meet
- Davis's converse of the Knaster–Tarski theorem
- Double layer potential
- Koebe's theorem on the mean value property
- Area-minimizing current
- Large deviations theory
- Compactness of families of harmonic functions
- McShane–Whitney extension
- Complete lattice
- Gradient estimates for harmonic functions
- Poisson integral formula
- Riemannian distance
- Green's identities
- Least harmonic majorant
- Liouville's theorem for harmonic functions
- Packing measure
- Sanov's theorem
- Wasserstein metric
- Knaster–Tarski theorem
- Cramér's theorem
- Liouville's theorem for planar harmonic functions
- Gauss's law for potentials
- Lévy–Prokhorov metric
- Graph embedding
- Hausdorff dimension
- Completeness in order theory
- Parabolic and hyperbolic Riemann surfaces
- Poisson integral for the half-space
- Metric outer measure
- Bôcher's theorem
- Hartogs lemma for subharmonic functions
Further reading
- Web https://en.wikipedia.org/wiki/Infimum_and_supremum, Formal definition
About this page
| Tag | 0QF1MZ9FRG |
|---|---|
| URI | m2://0QF1MZ9FRG |
| Aliases | greatest-lower-bound, inf |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A06 |
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What this page needs for W1
- an inventory row: the row of the inventory that the node accounts for (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Jordan measure
- Hausdorff measure
- Conditionally complete lattice
- Hausdorff distance
- Injectivity radius
- Join and meet
- Large deviations theory
- McShane–Whitney extension
- Complete lattice
- Riemannian distance
- Packing measure
- Wasserstein metric
- Knaster–Tarski theorem
- Lévy–Prokhorov metric
- Hausdorff dimension
- Completeness in order theory
- Metric outer measure