Let f : (0,1) —>R be measurable( w.r.t. Lebesgue measure) function in L1((0,1)). Define the function g on (0,1)× (0,1) by

g(x,y)=f(x)/x if 0<y<x<1

g(x,y)=0 if 0<x≤y<1

Prove:

1) g is measurable function (w.r.t. Lebesgue measure in the prodcut (0,1)× (0,1)

2)g is integrable in (0,1)× (0,1)