Measure theoretically equivalent

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When are two or more measures said to be measure theoretically equivalent?
I have spent sometime on searching it; I am not getting it. Please someone help.
 
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Well, start with the definition in your text, what is that?
(Since it is not widely-known terminology, we can only guess at it.)
 
I couldn't find this terminology in books. When I was reading a paper I-divergence geometry of distributions by I.CSISZAR, I came across this term. Initially I thought it could be mutually absolutely continuous; but its not. I couldn't make any guess.
 
For original Zeta function, ζ(s)=1+1/2^s+1/3^s+1/4^s+... =1+e^(-slog2)+e^(-slog3)+e^(-slog4)+... , Re(s)>1 Riemann extended the Zeta function to the region where s≠1 using analytical extension. New Zeta function is in the form of contour integration, which appears simple but is actually more inconvenient to analyze than the original Zeta function. The original Zeta function already contains all the information about the distribution of prime numbers. So we only handle with original Zeta...
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