Let f be Riemann integrable on J and let f(x) > 0 for x € J. Show that
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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22.N
Transcribed Image Text:9.8 BAIRE's THEOREM. If {H:k € N} is a countable family of closed
subsets of RP whose union contains a non-void open set, then at least one
of the sets Hr contains a nom-void open set.
Transcribed Image Text:22.N. Let f be Riemann integrable on J and let f(x) > 0 for x € J. Show that
0.
296
CH. VI INTEGRATION
(Hint: for each n € N, let H,, be the closure of the set of points x in J such that
f(x) > 1/n and apply Baire's Theorem 9.8.)
22.0. If f is Riemann integrable on I and if
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