Borel Function
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SOLVED: 1.5.4 Theorem: If h1, h2 are Borel measurable functions from R to R and hn (@) h(@) for all @ € R, then h is Borel measurable.Proof: It is sufficient to show that x: h(x) > c € B for each real number c. We havex: h(x) > c = c: lim hn (x) > c ∩ x: hn (x) is eventually > c for some n = 1,2,...= c: lim inf x: hn (x) > c = x: h(x) > c Therefore, h is Borel measurable.
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