Two or more measures are said to be measure theoretically equivalent when they assign the same measure to all measurable sets. This concept is crucial in probability theory and measure theory, particularly in the context of mutual absolute continuity. The term "measure theoretically equivalent" is not widely recognized in standard texts, but it is referenced in advanced literature, such as I. Csiszar's paper on I-divergence geometry of distributions. Understanding this concept requires familiarity with foundational measure theory principles.
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