Abstract
This chapter discusses integrals that are dependent on a parameter. An integral that converges uniformly for any λ in a certain interval will be a continuous function of λ in that interval. If it is possible, over the whole of this interval, to choose the open set σ (ɛ) to be the same and independent of the value of λ, then the integral will be uniformly convergent over the whole interval in the sense of the usual definition in analysis. In some cases, it is convenient to generalize the concept of uniform convergence of the integral for a given value of parameter to meet the situation.
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