Let f:[a,b]-> R be an integrable function.

Show that the graph of f in R^2 has zero content.

(hint: given a partition P of [a,b], interpret Spf-spf as a sum of areas of rectangles that cover the graph of f. )

Not sure where to start, any help?

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- February 27th 2011, 05:45 AMcalculuskid1zero content
Let f:[a,b]-> R be an integrable function.

Show that the graph of f in R^2 has zero content.

(hint: given a partition P of [a,b], interpret Spf-spf as a sum of areas of rectangles that cover the graph of f. )

Not sure where to start, any help? - February 27th 2011, 06:02 AMFernandoRevilla
:*Hint*

integrable in iff for every there exists a partition of such that .