User:Tdiagana

A function f: R→ X where (X, ||.||) is a Banach space, is said to be (Bohr) almost periodic if for all Є > 0 there exists l(Є) > 0 such that every interval of length l(Є) contains ς such that ||f(t+ς) - f(t)|| < Є for all t ε R.

A function f: R→ X where (X, ||.||) is a Banach space, is said to be (Bochner) almost periodic if for any sequence of real numbers {sn}n there exists a subsequence {t n}n of {s n}n such that f(t+t n) converges uniformly as n goes to infinity.