  In the present paper, after recalling the Karcher mean in Hadamard spaces, we
study the relation between convergence, almost convergence and mean convergence
(respect to the defined mean) of a sequence in Hadamard spaces. These results
extend Tauberian conditions from Banach spaces to Hadamard spaces. Also, we
show that every almost periodic sequence in Hadamard spaces is almost
convergent.
