content_image/327589.jpg content_image/327590.jpg content_image/327591.jpg content_image/327592.jpg content_image/327593.jpg
where F$_{˜}$ ψ ( X$_{j}$$_{+}$$_{τ}$$_{n}$ $_{)}$( x ) := P ( ˜ ψ ( X$_{j}$$_{+}$$_{τ}$$_{n}$ ) ≤ x ) and ˜ ψ := h − 1 ◦ ψ . 

Proof. Define 

<img src='content_image/327589.jpg'>

Then 

<img src='content_image/327590.jpg'>

Since { τ$_{n}$ = k } is measurable with respect to F j for all j ≥ k , it follows that 

<img src='content_image/327591.jpg'>

where ˜ ψ := h − 1 ◦ ψ . Furthermore, 

For i < j 

<img src='content_image/327592.jpg'>

<img src='content_image/327593.jpg'>

