  The deleting items theorems of weak law of large numbers (WLLN),strong law of
large numbers (SLLN) and central limit theorem (CLT) are derived by
substituting partial sum of random variable sequence with deleting items
partial sum. We address the background of deleting items limit theory of random
variable sequence, discuss the classical limit theory of Chebyshev WLLN,
Bernoulli WLLN and Khinchine WLLN with standard mathematical analytical
technique, then develop the deleting items theorems of WLLN, SLLN and CLT based
on convergence theorems and Slutsky's theorem. Our theorems extend the
classical limit theory of random variable sequence and provide the construction
of some asymptotic bias estimators of sample expectation and variance.
