P7 Given a set 2i and a measurable space (S2, F2), let f : N1 → 2. Fi = {f-'(B) : B e F2}. (1) %3D Show that Fi is a o-field and that f is measurable with respect to Fi and F2. Such F1 is called the o-field generated by f and it is denoted by o(f).

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P7
Given a set N1 and a measurable space (N2, F2), let
f : N1 → N2.
F1 = {f-l(B) : BE F2}.
(1)
Show that Fi is a o-field and that f is measurable with respect to Fi and
F2. Such F1 is called the o-field generated by f and it is denoted by
o(f).
Transcribed Image Text:P7 Given a set N1 and a measurable space (N2, F2), let f : N1 → N2. F1 = {f-l(B) : BE F2}. (1) Show that Fi is a o-field and that f is measurable with respect to Fi and F2. Such F1 is called the o-field generated by f and it is denoted by o(f).
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