Map for simultaneous measurements for a quantum logic

In this paper we will study a function of simultaneous measurements for quantum events (s-map) which will be compared with the conditional states on an orthomodular lattice as a basic structure for quantum logic. We will show the connection between s-map and a conditional state. On the basis of the Renyi approach to the conditioning, conditional states, and the independence of events with respect to a state are discussed. Observe that their relation of independence of events is not more symmetric contrary to the standard probabilistic case. Some illustrative examples are included.