Let be a smooth map between two manifolds. We call a regular point provided the derivative is non singular, so that there exists a neighbourhood of such that it is diffeomorphically mapped onto its image.(See Inverse function theorem) A point is called a regular value if contains only regular points. Otherwise we call them crtitical […]
Category: Analysis
Construction of measures using random variables
A common problem in measure theory is that we want to build a measure whose values are already morally clear on some small family of sets. We do not usually discover a measure by assigning values to arbitrary sets one by one. Instead, we begin with a simple class of sets where the desired answer […]
