Let S be a (Lebesgue) measurable subset of R and let f.g: S R be measurable...

Transcribed Image Text:

Let S be a (Lebesgue) measurable subset of R and let f.g: S→ R be measurable functions. Prove that (i) f + g is measurable and (ii) if o E C(R), then (f) is measurable. (b) Let f [a, b] → [-00, ∞] be a measurable function. Suppose that f takes the value to only on a set of (Lebesgue) measure zero. Prove that for any e > 0 there is a positive number M such that f≤ M, except on a set of measure less than €. Let S be a (Lebesgue) measurable subset of R and let f.g: S→ R be measurable functions. Prove that (i) f + g is measurable and (ii) if o E C(R), then (f) is measurable. (b) Let f [a, b] → [-00, ∞] be a measurable function. Suppose that f takes the value to only on a set of (Lebesgue) measure zero. Prove that for any e > 0 there is a positive number M such that f≤ M, except on a set of measure less than €.

Answer rating: 100% (QA)

The detailed ... View the full answer