Few today would dispute that the age of autonomous machines is nearly upon us (cf., Kurzweil, 2005; Moravec, 1988), if it not already. While doubtful one can identify any fully autono...

Some versions of the formula of integration by parts with respect to the Henstock-Kurzweil and the Henstock-Stieltjes integrals in Riesz spaces are given.

Introduction. The primary purpose of this note is to construct a C* Lyapunov function for a continuous vector field which has an asymptotically stable invariant set. Since there already exist techniques for constructing continuous Lyapunov functions with continuous derivatives by the vector field, our problem is simply to smooth such a function in such a way that the desired derivative properti...

The existing proofs of the Fundamental theorem of calculus for Lebesgue integration typically rely either on the Vitali–Carathéodory theorem on approximation of Lebesgue integrable functions by semi-continuous functions (as in [3, 9, 12]), or on the theorem characterizing increasing functions in terms of the four Dini derivates (as in [6, 10]). Alternatively, the theorem is derived using the Pe...