Let be a measure space, some measure. There exists at least one Lebesgue integrable function. Then does it hold that, ?
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What exactly are you asking? As for the last part you can just take to be the zero measure (not interesting but a measure none the less).
Originally Posted by putnam120 What exactly are you asking? As for the last part you can just take to be the zero measure (not interesting but a measure none the less). It's okay - I found an example (although I can't remember what it is...). Basically, my question was: does there exist a (positive) measure such that but which is not the zero measure.
Hello, Well just make a Dirac measure
Let be any measure defined on such that there exists with . Then the measure will be finite.
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