Sentence examples for defining a norm from inspiring English sources

By defining a norm, particular Banach spaces of functions can be considered.

Clearly, one may define a norm on C ( [ a, b ], R n ) to make it a normed vector space.

We show that if Xt is a continuous martingale with X0 = 0 then the quantity supt E Xtlog(Mt+Mt−)) defines a norm on H1 martingales equivalent to the usual norm.

We note that the expression defines a norm on.

If is a Young function, then defines a norm in, which is called the Luxemburg norm.

We define a norm, the so-called Luxemburg norm, on this space by the formula (1.4).

Now, we define a norm in E by |x|_{omega}=sup_{tgeq0}big| e^{omega t}S t)xbig|.

It is easy to show that (|cdot|_{X_{T}}) defines a norm on (X_{T}).

It is easy to verify that (3) defines a norm on (f(bar{N})).

If φ is a Young function, then || · || φ defines a norm in L φ, which is called the Luxemburg norm.

The following formula defines a norm in (L_{rho}) (frequently called Luxemburg norm): |f|_{rho} = infbigl{ alpha>0; rho(f/alpha leq1 bigr}.