3. Let {gn} be a sequence of integrable functions such that gn → g a.e. with g integrable. Show that lim fgn – g| = 0 if and only if lim f [gn| = S \g] .

Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. Absolute maximum at 5, absolute minimum at 2, local maximum at 3, local minima at 2 and 4 y y 3.0 2.5 2.0 1.5 1.0 0.5 y 3.0 2.5 2.0 1.5 1.0 0.5 W и 1 2 1 ^ 3 2 3 4 5 4 5 6 X X 2.5 W 2.0 1.5 3.0 1.0 0.5 y 3.0 2.5 2.0 1.5 1.0 0.5 1 T 2 3 2 3 4 5 4 5 сл 6 X X

#4

prove if this 2 statments are true or not.