By establishing large deviations on studentized increments of partial sums,the author proves studentized Hanson-Russo type increment theorem for all distributions in the domain of attraction of a stable law.

• 该文通过建立关于部分和学生化增量的大偏差不等式 ；在稳定律吸引场中证得了学生化的 Hanson- Russo型增量定理 .