Let be measures on such that and . Show that exists and satisfies a.e .

(Hint: and implies .

i do not have any idea how to do this. any help would be appreciated.

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- Jan 8th 2010, 03:02 PMKat-MRondon Nikodym derivative
Let be measures on such that and . Show that exists and satisfies a.e .

(Hint: and implies .

i do not have any idea how to do this. any help would be appreciated. - Jan 9th 2010, 01:47 AMShanks
since ,therefore .

the Radon Nikodym Theorem asserts that exist.

similarly,since exist.

Therefore,

therefore a.e.[\lambda]

since g is nonnegative, which implies , a.e.[\lambda].