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(Solved): Does d(x,y)=\int_a^b |x(t)-y(t)|dt define a metric or pseudometric on x if x is (i) the set of all r ...



Does

d(x,y)=\int_a^b |x(t)-y(t)|dt

define a metric or pseudometric on

x

if

x

is

(i)

the set of all real-valued continuous functions on

a,b

, (ii) the set of all real-valued Riemann integrable functions on

a,b

?



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