Parametrized Measures and Variational Principles

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver­ gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under­ stand weak convergence and its