For example, may be defined so that the iterated limits and exist and are equal for all x, and yet the Pringsheim limit does not exist. Possibility of commuting limit operations.
Pringsheim Convergence and the Dirichlet FunctionĬonvergence, Pointwise Limit, Double Sequence, Pringsheim, Dirichlet Function, Baire Category Theorem, CosineĪBSTRACT: Double sequences have some unexpected properties which derive from the (1976) Principles of Mathematical Analysis.
