Filter

Ok, let's break it down.

First, - to find today as a date we use the date() function, to which we can add days using addDays().
Next we need to figure out how to take a date and convert it to an element in the date column - you need to convert it to a timestamp and use StrToDate:

StrToMember([Dates].[Date],DateToTimeStamp(date())) /* today */
StrToMember([Dates].[Date].[dt],DateToTimeStamp(addDays(date(),-1))) /* yesterday */

The next step is to find out what day it is today - you can use DateFormat() function with "E" for the masking to receive the abbreviated day name.

and lastly - you need to use an if statement:

{if(
DateFormat(date(), "E") = "Mon",
{StrToMember([Dates].[Date],DateToTimeStamp(AddDays(date(),-3)))},
    if(DateFormat(date(), "E") = "Sun",
    {StrToMember([Dates].[Date],DateToTimeStamp(AddDays(date(),-2)))}, /* for Sunday - go back 2 days*/
    {StrToMember([Dates].[Date].[dt],DateToTimeStamp(AddDays(date(),-1)))} /* for any other case - go back 1 days*/
    )
)
}

I hope this helps,

Moshe