- #1
fderingoz
- 12
- 0
"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\rightarrowIR^{+} 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\rightarrowIR^{+} is continuous-?
What is it that i can not see ?
Several interesting nontrivial properties and ordering relations can be analyzed if a Young function \Phi:IR\rightarrowIR^{+} 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\rightarrowIR^{+} is continuous-?
What is it that i can not see ?
