カテゴリー: ノルム空間

\[ \left\Vert \boldsymbol{x}\right\Vert _{p}=\left(\sum_{j=1}^{n}\left|x_{j}\right|^{p}\right)^{\frac{1}{p}} \]

\[ \left(V\times W,\left\Vert \left(\boldsymbol{v},\boldsymbol{w}\right)\right\Vert _{V\times W}\right) \]

\[ c_{1}\left\Vert \boldsymbol{x}\right\Vert _{A}\leq\left\Vert \boldsymbol{x}\right\Vert _{B}\leq c_{2}\left\Vert \boldsymbol{x}\right\Vert _{A} \]

\[ \lim_{k\rightarrow\infty}\boldsymbol{x}_{k}=\boldsymbol{x}\Rightarrow\lim_{k\rightarrow\infty}\left\Vert \boldsymbol{x}_{k}\right\Vert =\left\Vert \boldsymbol{x}\right\Vert \]

\[ \forall\epsilon>0,\exists N\in\mathbb{N},N\leq n\rightarrow\left\Vert x_{n}-x\right\Vert <\epsilon \]

\[ d\left(\boldsymbol{x},\boldsymbol{y}\right)=\left\Vert \boldsymbol{x}-\boldsymbol{y}\right\Vert \]

\[ 0\leq\left\Vert \boldsymbol{v}\right\Vert \]

\[ \left(V,\left\Vert \bullet\right\Vert \right) \]