Math 2Formulary sheetFormulary sheet function spaces normed vectorspace ∀f∈V\forall f \in V∀f∈V the following should hold such that ∣∣⋅∣∣||\cdot||∣∣⋅∣∣ is a norm on VVV: ∣∣f∣∣<∞||f|| < \infty∣∣f∣∣<∞ ∣∣f∣∣≥0||f|| \ge 0∣∣f∣∣≥0 f≡0⟺∣∣f∣∣=0f \equiv 0 \Longleftrightarrow ||f|| = 0f≡0⟺∣∣f∣∣=0 ∀a∈R:∣∣af∣∣=∣a∣⋅∣∣f∣∣\forall a \in \R : ||af|| = |a| \cdot ||f||∀a∈R:∣∣af∣∣=∣a∣⋅∣∣f∣∣ ∀g∈V:∣∣f+g∣∣≤∣∣f∣∣+∣∣g∣∣\forall g \in V : ||f+g|| \le ||f|| + ||g||∀g∈V:∣∣f+g∣∣≤∣∣f∣∣+∣∣g∣∣