I have the following exercise, but i can't find the answer.Let ( X , A , μ ) be a measure space. Show that the measure μ is σ-finite, if there exists a function f ∈ M + ( X ) with f ( x ) &gt; 0 for all x ∈ X and ∫ X f d μ &lt; ∞.From what I understand is that the function f has to be from the set M + , so the set of strictly positive numeric functions (as defined in the script of the professor).

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I have the following exercise, but i can&#039;t find the answer.Let   (      X    ,      A    ,  μ  ) be a measure space. Show that the measure   μ is   σ-finite, if there exists a function   f  ∈            M        +    (      X    ) with   f  (  x  )  &amp;gt;  0 for all   x  ∈      X   and       ∫                  X              f  d  μ  &amp;lt;  ∞.From what I understand is that the function   f has to be from the set             M        +  , so the set of strictly positive numeric functions (as defined in the script of the professor).

Zayden Wiley · Accepted Answer

Let       A    n    =      f          −      1        (  [      n          −      1        ,  ∞  ]  ). We have       n          −      1        μ  (      A    n    )  ≤      ∫                  A        n              f  &amp;lt;  ∞ and       ⋃          n            A    n    =  X.

I have the following exercise, but i can't find the answer. Let ( <mrow class="MJX-TeXAtom-

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