# Young functions

by fderingoz
Tags: functions, young
 P: 12 "In his studies on Fourier Series, W.H.Young has analyzed certain convex functions $\Phi$:IR$\rightarrow$$\bar{IR}$$^{+}$ which satisfy the conditions : $\Phi$(-x)=$\Phi$(x), $\Phi$(0)=0, and lim$_{x\rightarrow\infty}$$\Phi$(x)=+$\infty$. Then $\Phi$ is called a Young function. Several interesting nontrivial properties and ordering relations can be analyzed if a Young function $\Phi$:IR$\rightarrow$IR$^{+}$ is continuous. "(rao-ren theory of orlicz spaces 1991) I think we can say from the definition of young function : Young functions are convex functions on IR and IR is a open convex set and we know also that if a funtion is convex on an open convex set then this function is continuous on that open set, So young functions are continuous. Why the authors needs to write second paragraph,i.e. -Several interesting nontrivial properties and ordering relations can be analyzed if a Young function $\Phi$:IR$\rightarrow$IR$^{+}$ is continuous-? What is it that i can not see ?

 Related Discussions Calculus 0 Advanced Physics Homework 0 Calculus 3 Precalculus Mathematics Homework 2 Set Theory, Logic, Probability, Statistics 4