On Some Pointwise Defects of Properties in Real Analysis
Adrian I. Ban, Sorin Gheorghe Gal · Real Analysis Exchange · 2004
In this paper we continue the research in Real Analysis, in the spirit of the very recent book [1]. Firstly, as a refinement of the global defect of integrability introduced in [1], $\\S $5.1, we consider here a pointwise defect of integrability and study its properties and connections with the pointwise defect of continuity already introduced in [1], $\\S$ 5.1. Secondly, as refinements of the global defects of monotonicity and of convexity introduced in the same book [1], $\\S$ 5.2, we consider and study pointwise variants