I am just wondering what the term 'independent equations' means.
I found the term in the book of Kolmogorov about the basic notions of probability calculus. After Definition I of Section ('paragraph') 5 of Chapter I, where independence of experiments are defined, he notes that (according to the translation to my language) 'from the r equations of formula (2), only r - (r1+...+rn)+(n-1) are independent". Moreover, there is a footnote, to this statement, counting the number of equations related to the number of independent variables and other constraining equations.
The meaning of 'independent linear equations' is clear: none of them can be expressed as a linear combination of the others. But the meaning of 'independent equations', i.e. generally 'independent nonlinear equations', is unclear to me.