Let $f$ be riemann stieltjes integrable w.r.t $a$;
let $g$ be a continious linear functional on $\mathscr{C}[a,b]$.
Then $g(f)= \int_{a}^{b} f da$.
Is it riesz thorem?
Can anyone refer any link to the proof of the theorem?
Any help would be appreciated .
Thanks in advance.
Can anyone please help me in proving the theorem.
Any help would be appreciated.
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Nobody is going to answer this with the current formatting. I recommend you retype this with Latex. – ADA May 27 '17 at 17:54
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For formatting tips, please see https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Angina Seng May 27 '17 at 17:55
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Yeah, OP, you're probably looking for this. – Chris May 27 '17 at 17:55
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1Or perhaps you want the original version proven by Riesz. – Chris May 27 '17 at 17:56
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Please do look through the formatting guide shared above. Also, it seems like inconsistent notation you're using.. the lower integral bound is $a$ and the variable you are integrating over is also $a$? $\int_a^b f , da$? – Tom May 27 '17 at 18:19
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From what you wrote, it is not the statement of Riesz theorem. Guess you misstated what you were after. By the way, the statement is false; it says that every linear functional is constant... – Yes May 27 '17 at 18:31
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1Riesz had many theorems.I did not meant one of the famous ones. – Math is beautiful May 27 '17 at 18:56