Describe the mistake
There is a slight formal problem in the definition of a multivariate expected value of z function g. Namely in the equation (6.30) on left hand side you write EX[g(\bf{x})] which suggests g is a function taking an argument from \mathbb{R}^D. On the other hand, on the right hand side of the same equation you write E{X_1}[g(x_1)] which clearly suggests g is a function taking a real argument.
Location
Please provide the
version Draft (2024-01-15)
Chapter 6, Section 6.4.1
Page: 187
Equation 6.30
Proposed solution
Clearly define what function g is and how should it be interpreted. In definition 6.3 you write g: R->R, which doesn't work in the multivariate case.
Describe the mistake There is a slight formal problem in the definition of a multivariate expected value of z function g. Namely in the equation (6.30) on left hand side you write EX[g(\bf{x})] which suggests g is a function taking an argument from \mathbb{R}^D. On the other hand, on the right hand side of the same equation you write E{X_1}[g(x_1)] which clearly suggests g is a function taking a real argument.
Location Please provide the
Proposed solution Clearly define what function g is and how should it be interpreted. In definition 6.3 you write g: R->R, which doesn't work in the multivariate case.