unconditional convergenceの例文

例文

1. For real series it follows from the Riemann rearrangement theorem that unconditional convergence implies absolute convergence.
2. Absolute convergence and convergence together imply unconditional convergence, but unconditional convergence does not imply absolute convergence in general, even if the space is Banach, although the implication holds in \ mathbb { R } ^ d.
3. Absolute convergence and convergence together imply unconditional convergence, but unconditional convergence does not imply absolute convergence in general, even if the space is Banach, although the implication holds in \ mathbb { R } ^ d.
4. Since a series with values in a finite-dimensional normed space is absolutely convergent if each of its one-dimensional projections is absolutely convergent, it follows that absolute and unconditional convergence coincide for "'R " "'n "-valued series.
5. When " X " & thinsp; is complete, then unconditional convergence is also equivalent to the fact that all subseries are convergent; if " X " & thinsp; is a Banach space, this is equivalent to say that for every sequence of signs " ? " " n " = ?, the series