Explore: Rearrangement Invariant Spaces

(nonsymmetric) decreasing rearrangement function arises often in the theory of rearrangement-invariant Banach function spaces. Especially important is

reason for merging space and time into spacetime is that space and time are separately not invariant, which is to say that, under the proper conditions, different

space-filling polyhedron if and only if its Dehn invariant is zero. The Dehn invariant of a self-intersection-free flexible polyhedron is invariant as

spaces, introduced by George G. Lorentz in the 1950s, are generalisations of the more familiar L p {\displaystyle L^{p}} spaces. The Lorentz spaces are

surface without stretching it. Thus the Gaussian curvature is an intrinsic invariant of a surface. Gauss presented the theorem in this manner (translated from

equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension

Sobolev energy of a function in a Sobolev space does not increase under symmetric decreasing rearrangement. The inequality is named after the mathematicians

function of the tile configuration that is invariant under any valid move and then using this to partition the space of all possible labelled states into two

separable infinite-dimensional Hilbert space and Calkin sequence spaces (also called rearrangement invariant sequence spaces). The correspondence is implemented

duality, vertex figures, surface area, volume, interior lines, Dehn invariant, and symmetry. A symmetry of a polyhedron means that the polyhedron's