Prove f is in L3(dμ): Measurable Function

[hedipaldi]

Let f be a measurable nonegative function on a positive measure space,such that for every positive t,
μ{x:f(x)≥t}≤M/(t^5)
M is constant.prove that f is in the space L3(dμ)

 

[Bacle2]

What have you tried so far? It basically comes down to showing that the third power of the absolute value converges. Use the inequality you have to show that the function slows down enough as t increases for f to be integrable.