Before revision:  Consider two portfolios, one is a passive buy-and-hold portfolio representing the entire market , and the other assigns a portfolio vector for each possible value of the market weights and requires trading to maintain this assignment.
After revision:  Consider two portfolios, one is a passive buy-and-hold portfolio called the market portfolio whose value represents the performance of the entire stock market. Consider a function that assigns a portfolio vector for each possible value of the market weights and requires trading to maintain this assignment.