Let X be a weakly $Lindel\ddot{o}f$ determined Banach space. We prove that if X is non-separable, then there exist a complete probability space (Ω, Σ, μ) and a ...

Abstract We prove that, in a weak sense, any integrable function on the real line tends to zero at infinity: if f is an integrable function on ¡, then for almost all real number x, the sequence (f(nx) ...