We prove an existence theorem for the equation x = f(t, xt), x(Θ) = φ(Θ), where xt(Θ) = x(t + Θ), for −r ≤ Θ < 0, t ∈ Ia, Ia = [0, a], a ∈ R+ in a Banach space, using the Henstock-KurzweilPettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose tha...

Distributional approaches to meaning acquisition utilize distributional properties of linguistic entities as the building blocks of semantics. In doing so, they rely fundamentally on a set of assumptions about the nature of language and meaning referred to as the distributional hypothesis. This hypothesis is often stated in terms like “words which are similar in meaning occur in similar context...