${\displaystyle {}f}$

${\displaystyle L(f)={\operatorname {sup} \,(L(f(t_{0}),\ldots ,f(t_{k})),a=t_{0}\leq t_{1}\leq \ldots \leq t_{k-1}\leq t_{k}=b{\text{ Unterteilung}},\,k\in \mathbb {N} )}.}$

${\displaystyle {}\varphi }$

${\displaystyle {}P}$

${\displaystyle {}\mathbb {R} }$

${\displaystyle {}L\colon \mathbb {R} ^{n}\rightarrow \mathbb {R} ^{m}}$

${\displaystyle {}\varphi (P+v)=\varphi (P)+L(v)+\Vert {v}\Vert r(v)\,}$

gibt, wobei ${\displaystyle {}r\colon U{\left(0,\delta \right)}\rightarrow W}$ eine in ${\displaystyle {}0}$ stetige Abbildung mit ${\displaystyle {}r(0)=0}$ ist und die Gleichung für alle ${\displaystyle {}v\in V}$ mit ${\displaystyle {}P+v\in U{\left(P,\delta \right)}\subseteq G}$ gilt.

${\displaystyle {}P}$

${\displaystyle {}\operatorname {rang} \,\left(D\varphi \right)_{P}={\min {\left(\dim _{}{\left(V\right)},\dim _{}{\left(W\right)}\right)}}\,}$

ist.

${\displaystyle {}P}$

${\displaystyle {\left\{v\in V\mid {\left(D\varphi \right)}_{P}{\left(v\right)}=0\right\}}.}$

${\displaystyle {}K}$

${\displaystyle {}V}$

${\displaystyle {}K}$

${\displaystyle {}\left\langle -,-\right\rangle }$

${\displaystyle {}V}$

${\displaystyle {}\left\langle v,w\right\rangle =\left\langle w,v\right\rangle \,}$

für alle ${\displaystyle {}v,w\in V}$ gilt.

${\displaystyle {}f}$

${\displaystyle {}c<1}$

${\displaystyle d{\left(f(x),f(y)\right)}\leq c\cdot d{\left(x,y\right)}}$

für alle ${\displaystyle {}x,y\in L}$.

${\displaystyle 0=V_{0}\subset V_{1}\subset \ldots \subset V_{n-1}\subset V_{n}=V}$

heißt eine Fahne in ${\displaystyle {}V}$.