“Natural” finite measure over continuous probability densities over the interval [0,a]

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I wonder whether there is a "natural" finite measure μ
(such as the Lebesgue-Measure on R∩[0,a]) over the space of all continous probability density functions on [0,a]







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    What do you mean by "natural"? There is certainly no obvious choice.
    – Robert Israel
    Aug 8 at 19:31










  • I'd think that if there was a "natural" choice, that'd be the one that would be taught most of the time, no? The fact that there isn't such a choice taught should tell you something.
    – Rushabh Mehta
    Aug 8 at 19:45














up vote
0
down vote

favorite












I wonder whether there is a "natural" finite measure μ
(such as the Lebesgue-Measure on R∩[0,a]) over the space of all continous probability density functions on [0,a]







share|cite|improve this question
















  • 1




    What do you mean by "natural"? There is certainly no obvious choice.
    – Robert Israel
    Aug 8 at 19:31










  • I'd think that if there was a "natural" choice, that'd be the one that would be taught most of the time, no? The fact that there isn't such a choice taught should tell you something.
    – Rushabh Mehta
    Aug 8 at 19:45












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I wonder whether there is a "natural" finite measure μ
(such as the Lebesgue-Measure on R∩[0,a]) over the space of all continous probability density functions on [0,a]







share|cite|improve this question












I wonder whether there is a "natural" finite measure μ
(such as the Lebesgue-Measure on R∩[0,a]) over the space of all continous probability density functions on [0,a]









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 8 at 19:27









0rangetree

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  • 1




    What do you mean by "natural"? There is certainly no obvious choice.
    – Robert Israel
    Aug 8 at 19:31










  • I'd think that if there was a "natural" choice, that'd be the one that would be taught most of the time, no? The fact that there isn't such a choice taught should tell you something.
    – Rushabh Mehta
    Aug 8 at 19:45












  • 1




    What do you mean by "natural"? There is certainly no obvious choice.
    – Robert Israel
    Aug 8 at 19:31










  • I'd think that if there was a "natural" choice, that'd be the one that would be taught most of the time, no? The fact that there isn't such a choice taught should tell you something.
    – Rushabh Mehta
    Aug 8 at 19:45







1




1




What do you mean by "natural"? There is certainly no obvious choice.
– Robert Israel
Aug 8 at 19:31




What do you mean by "natural"? There is certainly no obvious choice.
– Robert Israel
Aug 8 at 19:31












I'd think that if there was a "natural" choice, that'd be the one that would be taught most of the time, no? The fact that there isn't such a choice taught should tell you something.
– Rushabh Mehta
Aug 8 at 19:45




I'd think that if there was a "natural" choice, that'd be the one that would be taught most of the time, no? The fact that there isn't such a choice taught should tell you something.
– Rushabh Mehta
Aug 8 at 19:45















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