  We reprove Wolff's $L^{\frac{5}2}-$ bound for the $\R^3-$Kakeya maximal
function without appealing to the argument of induction on scales. The main
ingredient in our proof is an adaptation of Sogge's strategy used in the work
on Nikodym-type sets in curved spaces. Although the equivalence between these
two type maximal functions is well known, our proof may shed light on some new
geometric observations which is interesting in its own right.
