Let g be a fixed monotone increasing function on J=[a, b]. If f is any function which is integrable with respect to g on J, then we define f1 by f1=^b|f| d g . Show that the following "norm properties" are satisfied: (a) f1 ≥0; (b) If f(x)=0 for all x ∈J, then f1=0; (c) If c ∈𝐑, then f f1=|c|f1; (d) |f1-h1| ≤|| f ±h1 ≤ f1 h 1. However, it is possible to have f1=0 without having f(x)=0 for all x ∈J. (Can this occur when g(x)=x ?) | Numerade
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