Moment Generating Function determines the distribution statement

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So I have been given the following definition of the theorem of MGF determining distribution:

Given 2 random variables X and Y if there exists a>0 such that Mx(t) and My(t) are finite and coincide for x $\in$ [-a,a] then X and Y have the same distribution

I am not sure about the significant of coincide for x $\in$ [-a,a].

Thank you?