This might not be the right subforum, but I was told that measure theory is very important in probability theory, so I thought maybe it belonged here.(adsbygoogle = window.adsbygoogle || []).push({});

I am confused about the difference between ameasure(which is afunctiononto [itex]\mathbb{R}[/itex] that satisfies the axioms listed here: https://proofwiki.org/wiki/Definition:Measure_(Measure_Theory) ) andmeasurability(which is acriteriathat a function onto [itex]\mathbb{R}[/itex] can meet. These criteria are listed here: https://proofwiki.org/wiki/Definition:Measurable_Function ). I'm assuming these things are related, but the definitions seems so different so I don't really understand the relation between them. For example, if a function f is sigma measurable, is there automatically some "measure function" we can derive from it? Or similarly, is a measure always sigma measurable?

Also - I was curious, is there a difference between being "sigma measurable" and just "measurable?" The things I was reading seemed to use the terms interchangeably, so I just wasn't certain. Sorry if these questions are kind of dumb and obvious, I am brand new to measure theory and still trying to wrap my head around these definitions

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# Can someone help me understand the difference between a measure, and a function which is measurable?

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