Banach space
normed vector space that is complete
abstract Wiener space
separable Banach space equipped with a Hilbert subspace such that the standard cylinder set measure on the Hilbert subspace induces a Gaussian measure on the whole Banach space
Hilbert space
inner product space that is metrically complete; a Banach space whose norm induces an inner product (follows the parallelogram identity)
uniformly convex space
reflexive Banach space such that the center of a line segment inside the unit ball must lie deep inside the unit ball unless the segment is short
Banach lattice
Banach space with a compatible structure of a lattice
set of real numbers
set whose elements are the real numbers