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I have a simple question as follows:

[itex]f[/itex] is a function from [itex]X[/itex] to [itex]Y[/itex] where

[itex]X=[0,1][/itex]; and

[itex]Y[/itex] is finite, i.e. [itex]\vert Y\vert <\infty[/itex]

then is [itex]f[/itex] Borel measurable?

Thank you for your help in advance.