Definitions. Example In the sup-norm, C[0;1] is a Banach space (convergence in the sup-norm is exactly the concept of uniform Example Under either norm in Example, Rnis a Banach space. In the following two de nition we identiy two functions if they are equal to each other -a.e(i) ForpLp() space to be the normed space of (equivalence classes of) measurable functions on Xsuch that jjfjj p:= Z X jfjpd 1=p <1 De nition A Banach space is a vector space V equipped with a norm jjjjsuch that, with respe