The strong law under a semiparametric model for truncated and censored data

In this paper we study integrals for any nonnegative measurable functions with respect to semiparametric estimators of the survival function and the cumulative hazard function based on left truncated and right censored data. The strong law of large numbers for these integrals is given. The results are useful in establishing strong consistency of many estimators under the semiparametric model for truncated and censored data.