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Share-Based Payments - Exercisable Options (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Compensation expense      
Allocated Share-based Compensation Expense $ 73.1 $ 83.8 $ 73.4
Unrecognized compensation expense $ 94.3 96.8  
Vesting period 3 years    
Employee Stock Option      
Stock Incentive Plans, additional disclosures      
Aggregate intrinsic value of stock options exercised $ 0.9 $ 1.2 $ 0.6
Compensation expense      
Number of stock options granted during the period 0 0  
Performance Earnings Program      
Compensation expense      
Weighted average grant-date fair value of stock options granted (in dollars per share) $ 37.69 $ 38.15 $ 29.91
Performance period over which objectives must be met to qualify for an award grant 3 years    
Restricted Stock Units (RSUs)      
Compensation expense      
Weighted average grant-date fair value of stock options granted (in dollars per share) $ 36.83 $ 37.96 $ 29.82
$31.62 | Employee Stock Option      
Options Outstanding      
Number outstanding as of end of period (in shares) 600,000    
Weighted Average Remaining Contractual Life 5 years 5 months 5 days    
Weighted Average Exercise Price (in dollars per share) $ 31.62    
Aggregate Intrinsic Value (in millions) $ 0.7