Thread: Measuring the reals

Let be a measure space, some measure. There exists at least one Lebesgue integrable function. Then does it hold that,

?

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.