Hlders inequality for a pair of random variables X and Y is E |XY | {E|X|

Hölder’s inequality for a pair of random variables X and Y is E |XY | ≤ {E|X|

p}

1/p{E|Y |

q}

1/q where p−1 + q−1

= 1. Deduce from the above that

{E |X1X2 …Xr|}

r ≤ E|X1|

r …E|Xr|

r for random variables X1, …,Xr

. Hence prove that if the diagonal elements of cumulant tensors are finite then all other elements are finite.