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How can we prove an inequality of integrable step functions:

More Precisely: Integral of max{a,b} > max {integral a, integral b}

Any initial help would be appreciated.

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Draw a picture! Seriously, you are more likely to get a pertinent answer on one of the sites mentioned in the FAQ: mathoverflow.net/faq#whatnot – Andrew Stacey Apr 27 2010 at 14:30
Sorry, I am just looking for way for a proof into which to focus ... not an answer – Andrey Apr 27 2010 at 14:34
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 In that case, my suggestion is not facetious: draw a picture. Specifically, find some very simple step functions and draw the situation for those. I recommend, in particular, finding two step functions, say a and b, with a(x) > b(x) some of the time and b(x) > a(x) some of the time and drawing the graphs of a, b, and max{a,b}. – Andrew Stacey Apr 27 2010 at 14:55
Or just recall that $c\ge\max(a,b)$ is merely a fancy way to write $c\ge a$ and $c\ge b$ and that $\max(a,\text{anything})$ is certainly not less than $a$. – fedja Apr 27 2010 at 15:18

closed as too localized by Andrew Stacey, Reid Barton, David Speyer, fedja, Gerald Edgar Apr 27 2010 at 15:36

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