On the Rearrangement of Conditionally Convergent Series
C. T. Rajagopal · Annals of Mathematics · 1941
In an earlier note [6], I have shown that the idea behind the theorem-that of a condensation effected on series by integrating a suitable function over intervals of the type (D.-,, D,)-supplies the basis for a unified theory of convergence criteria for series of positive terms, more comprehensive than Pringsheim's [3] in certain respects. In another note [7], I have shown that the idea suggests elegant proofs of certain classic theorems of Pringsheim [4]. I prove here that the same idea can be used to generalize the enunciations and simplify the proofs of Pringsheim's theorems concerning the rearrangement of conditionally convergent series [5].2