Let f ε L1(T). Define fα by fα(x) = f(x + α). Then the Fourier series of f is absolutely convergent if and only if there exists a Lebesgue point α for f such that both sequences $\langle(R_e ...

In the fifth century B.C., the Greek philosopher Zeno of Elea attempted to demonstrate that motion is only an illusion by proposing the following paradox: Achilles the warrior is in a footrace with a ...

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches ...