1/17/2024 0 Comments Cauchy sequence divergence![]() Šalát, T., On statistically convergent sequences of real numbers, Math. Kostyrko, P., Šalát, T., Wilczyński, W., I-Convergence, Real Anal.Dems, K., On I-Cauchy sequences, Real Anal.(2008) MR2458252 DOI10.14321/realanalexch. First quarter of three-quarter honors integrated linear algebra/multivariable calculus sequence for well-prepared students. I wonder if a Cauchy sequence (which is not convergent in a non-complete normed space) is still called a divergent sequence. Das, P., Malik, P., 10.14321/realanalexch., Real Anal. All of them define divergent sequence as a sequence which is not convergent.(2006) Zbl1092.40001 MR2241135 DOI10.1016/j.jmaa.2005.07.067 Be able to deduce from the theory of sequences basic convergence tests: Cauchy test, divergence test, absolute convergence test. A sequence that does not converge is said to be divergent. ![]() If such a limit exists, the sequence is called convergent. A., Orhan, C., 10.1016/j.jmaa.2005.07.067, J. In mathematics, the limit of a sequence is the value that the terms of a sequence 'tend to', and is often denoted using the symbol (e.g., ). Connor, J., R-type summability methods, Cauchy criterion, P-sets and statistical convergence, Proc.Balcerzak, M., Dems, K., 10.14321/realanalexch., Real Anal.LA - eng KW - double sequences $\mu $-statistical convergence divergence and Cauchy criteria convergence divergence and Cauchy criteria in $\mu $-density condition (APO$_2)$ double sequence -statistical convergence divergence criteria Cauchy criteria convergence -density condition (APO UR - ER. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure $\mu $ has the condition (APO$_2$). We then introduce a property of the measure $\mu $ called the (APO$_2$) condition, inspired by the (APO) condition of Connor. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. TY - JOUR AU - Das, Pratulananda AU - Bhunia, Santanu TI - Two valued measure and summability of double sequences JO - Czechoslovak Mathematical Journal PY - 2009 PB - Institute of Mathematics, Academy of Sciences of the Czech Republic VL - 59 IS - 4 SP - 1141 EP - 1155 AB - In this paper, following the methods of Connor, we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely ) to $\mu $-statistical convergence and convergence in $\mu $-density using a two valued measure $\mu $.
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