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Suppose

`f,g:E->R`

are measurable functions on a sigma algebra

`E`

. Show that

`h:E->R`

defined by

`h(x)={((f(x))/(g(x)) if g(x)!=0),(0, If g(x)=0):}`

is measurable. 6. Let

`Nsub[0,1]`

be a non-measurable set. Determine whether the function

`f:R->R`

defined by

`f(x)={(x if xinN),(-x, If x!inN):}`

is measurable. Explain