Given that two functions $f$ and $g$ from $\Bbb R$ to $\Bbb R$, such that $f$ is non-increasing and $g$ is non-decreasing. How does one show that the function $f+g$ is Borel measurable?
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I haven't bought the book yet, since the semester hasn't started yet. I am just trying to get a head start in this course of mine. Are you going to contribute with an help hand or just pointing fingers? – Zacharias Heindriksonnir Aug 23 '18 at 17:44
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have a look here: https://math.stackexchange.com/q/252421/144410 – user144410 Aug 23 '18 at 17:56
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Thank you, but i just got more confused. – Zacharias Heindriksonnir Aug 23 '18 at 18:23
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If f and g are both Borel measurable, then the sum is also (known theorem). – herb steinberg Aug 23 '18 at 19:51
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@herbsteinberg, can you link me the theorem or refer me where to find it? – Zacharias Heindriksonnir Aug 27 '18 at 17:47
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Could anyone perhaps provide me a suitable solution with justifying steps? – Zacharias Heindriksonnir Aug 27 '18 at 17:57
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https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes_ch3.pdf https://sites.ualberta.ca/~rjia/Math417/Notes/chap5.pdf Google "sum of borel measurable functions" to get others. – herb steinberg Aug 27 '18 at 19:36