Sentence examples for monotone norm from inspiring English sources

Let Φ be a normed space of Lebesgue measurable functions, defined on ((0,infty)), with monotone norm: (|g|leq |h|) implies (|g|_{Phi}leq |h|_{Phi}).

The monotone norm ?

Hence, ∥ ⋅ ∥ is a monotone norm.

The convergence in Y is generated by a monotone norm on Y.

Then there exists a monotone norm ∥ ⋅ ∥ on Y such that the following statements hold true.

· ? is a monotone norm on Y which can be defined by ?

Therefore, taking into account that the Schauder bases considered are monotone (norm-one projections, see [21]), we arrive at (3.15).

By definition, the K-interpolation space A Φ = ( A 0, A 1 ) Φ has a quasi-norm ∥ f ∥ A Φ = ∥ K ( t, f ) ∥ Φ, where Φ is a quasi-normed function space with a monotone quasi-norm on ( 0, ∞ ) with the Lebesgue measure and such that min { 1, t } ∈ Φ.

More precisely, we consider quasi-norm rearrangment invariant space E, consisting of functions (fin L^{1}+L^{infty}), such that the quasi-norm (|f|_{E}=rho (f^{ast})<infty), where (rho_{E}) a monotone quasi-norm, defined on (M^) with values in ([0,infty]).

Let (rho_{H}) be a monotone quasi-norm on (M^) and let H be the corresponding quasi-normed space, consisting of all locally integrable functions on ((0,1)) with a finite quasi-norm (|g|_{H}=rho_{H} |g|)).

Let (rho_{E}) be a monotone quasi-norm on (M^) and let E be the corresponding rearrangement invariant quasi-normed space consisting of all (fin L^{1}(Omega)) such that (|f|_{E}=rho_{E}(f^{ast})<infty).