2

In Rudin

Measurable function are defined as

$(X,M)$ is measurable space , $(U,\tau)$ is topological space f is said to be measurable function if for every open set $v\in \tau$ in U $f^{-1}(v)\in M $

In folland

Measurable function are defined as

$(X,M),(Y,N)$ are measurable spacef is said to be measurable function if for every open set $v\in N$ then $f^{-1}(v)\in M $ (i.e inverse image of measurable set is measurable )

I know that Measurable set and topological are different concept No one implies one another

So are they equivalent or not ?

Any Help will be appreciated

Curious student
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    First definition is special case of second definition, when $Y$ is topological space and $N$ is Borel sigma-algebra. To see that it is a special case, note that $f^{-1}(v) \in M$ for any open $v$ is equivalent to $f^{-1}(v) \in M$ for any Borel set $v$. To see that equivalence, just note that ${v : f^{-1}(v) \in M}$ is a sigma-algebra. – mathworker21 May 28 '19 at 14:12
  • Your this question was just deleted by some very nice people. – peterh May 28 '19 at 22:39
  • @peterh Thanks Sir actually I had no idea about that before. – Curious student May 29 '19 at 02:38

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