We prove a contraction property of Fock type spaces L_α^p of log-subharmonic functions in Rⁿ. To prove the result, we demonstrate a certain monotonic property of measures of the superlevel set of the function

u(x) = |f(x)|^p e^-(α/2)p|x|2,

provided that f is a certain log-subharmonic function in R^m. The result recover a contraction property of holomorphic functions in the Fock space F_α^p proved by Carlen in [Car1991].

After I proved my main results, Kehe Zhu directed me to the reference by Carlen [Car1991], for which I am thankful. I am also grateful to Djordjije Vujadinovic for his valuable insights and discussions on the topic.