The power condensation test of the convergence of positive double series with monotone decreasing terms
Basic notions of the theory of double series and their properties are presented. A few definitions of double series are given. Positive double series and convergence tests are considered. The basic test of convergence of the positive double series, based on the condition to have the upper bound of the partial sums is given. New test for the boundedness of the partial sums is formulated. For the first time the power test of condensation for double series with positive and monotonically decreasing terms is proved, which is the analog of the well-known test of condensation by Schlömilch and test of condensation by Knopp - Tereshchenko for ordinary infinite series. An example of the use of this test is given.