I was reading a paper, and they wrote μ ( f ) where μ is a measure and f a function. I know measures map sets to nonnegative numbers, but I don't know what it means to write μ ( f ).

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I was reading a paper, and they wrote   μ  (  f  ) where   μ is a measure and   f a function. I know measures map sets to nonnegative numbers, but I don&#039;t know what it means to write   μ  (  f  ).

Darion Sexton · Accepted Answer

It&#039;s something of a guessing game without having a look at the paper itself, but   μ  (  f  ) is sometimes used to denote   ∫  f    d  μ. This notational convention is one of the ways people may use to express the action of a distribution on a test function. Another common way this gets expressed is in the notation  ⟨  μ  ,  f  ⟩  =  ∫  f    d  μ  .The   ⟨  μ  ,  f  ⟩ notation emphasizes the duality between distributions (in this case measures) and test functions.

I was reading a paper, and they wrote μ ( f ) where μ<!--

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