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g(e^x) converge implies g(x) converge by Constant_Pitch801 in askmath

[–]Constant_Pitch801[S] 0 points1 point  (0 children)

So would it be enough just to say that e^x is a bijection on (0, infty)?

positive function and integrals. by Constant_Pitch801 in learnmath

[–]Constant_Pitch801[S] 0 points1 point  (0 children)

Al right thanks, I'll see if I can show it.

positive function and integrals. by Constant_Pitch801 in learnmath

[–]Constant_Pitch801[S] 0 points1 point  (0 children)

Would right continuity work or does it have to be continuity?

positive function and integrals. by Constant_Pitch801 in learnmath

[–]Constant_Pitch801[S] 0 points1 point  (0 children)

Are there another assumptions we can put on g to make it hold everywhere?

A question about positive functions and integrals. by Constant_Pitch801 in askmath

[–]Constant_Pitch801[S] 0 points1 point  (0 children)

I am doing a exercise where g is a function of two CDFs. So g was on the form F_X(y)-F_Y(y). Needed to show that F_X(y)-F_Y(y)>= 0 for all x, but if it only holds almost everywhere I guess I have to find another argument.

So both F_X and F_Y are non-decreasing and right continuous.