  In this paper we present a series of seemingly unrelated results of Complex
Analysis which are in fact connected via a different approach to their proofs
using the results of Errett Bishop of volumes and limits of analytic varieties.
We start by proving Chow's theorem by a technique suggested long time ago in
the beautiful book by Gabriel Stolzenberg. We think this approach is very
attractive and easier for students and newcomers to understand; also the theory
presented here is linked to areas of mathematics that are not usually
associated with Chow's result. In addition, Bishop's results imply both Chow's
and Remmert-Stein's theorems directly, meaning that this view is simpler and
just as profound as Remmert-Stein's proof. After that, we give a comparison
table that explains how Bishop's theorems generalize to several complex
variables classical results of one complex variable and prove Montel's
compactness theorem using the techniques presented here. Finally we give an
alternative proof of a theorem of Edwards, Millet and Sullivan of foliations
with compact leaves for the case of complex foliations in K\"ahler manifolds.

Complex Variables