I was reading George Lowthers notes on Stochastic Calculus and , he says the following but I cannot figure out what it exactly means?
He writes the following after defining a Previsible Process and a Predictable $\sigma$-algebra
Given any set of real-valued functions on a set, which is closed under multiplication, the set of functions measurable with respect to the generated sigma-algebra can be identitified as follows. They form the smallest set of real-valued functions containing the generating set and which is closed under taking linear combinations and increasing limits. So, for example, the predictable processes form the smallest set containing the adapted left-continuous processes which is closed under linear combinations and such that the limit of an increasing sequence of predictable processes is predictable.