A Note on p-Adic Invariant Integral in the Rings of p-Adic Integers

In [2], I constructed the p-adic q-integral on Zp. In this paper, we consider the properties of the p-adic invariant p-adic q-integral in the ring of p-adic integers at q=-1. Finally we give the some applications of p-adic q-integration at q=-1. These properties are useful and worthwhile to study Euler numbers and polynomials.