 Hardy and J.E.Littlewood explained their maximal inequality in the language of cricket averages.Given a function "f" defined on R"n", the uncentred Hardy–Littlewood maximal function "Mf" of "f" is defined as

for each "x" in R"n", where the supremum is taken over all balls(nice) "B" and formula_2 is the integral average of formula_3 over the ball formula_4.