Riesz space [SEP] named after
Riesz space
In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice.
Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper "Sur la décomposition des opérations fonctionelles linéaires".
Riesz spaces have wide ranging applications. They are important in measure theory, in that important results are special cases of results for Riesz Spaces. E.g. the Radon–Nikodym theorem follows as a special case of the Freudenthal
Riesz potential
In mathematics, the Riesz potential is a potential named after its discoverer, the Hungarian mathematician Marcel Riesz. In a sense, the Riesz potential defines an inverse for a power of the Laplace operator on Euclidean space. They generalize to several variables the Riemann–Liouville integrals of one variable.
If 0 < α < "n", then the Riesz potential "I""f" of a locally integrable function "f" on R is the function defined by
where the constant is given